Short Answer, Nobody Knows for Sure
The long answer is that there is some evidence that might have happened at least once in Vulcan history, but the evidence is not strong enough to be proof.
Among the very first things we learn about Vulcan history is:
"The Conscience of the King":
MCCOY: Negative. Did you know this is the first time in a week I've had time for a drop of the true? Would you care for a drink, Mister Spock?
SPOCK: My father's race was spared the dubious benefits of alcohol.
MCCOY: Now I know why they were conquered. What are you so worried about, anyway? I find Jim generally knows what he's doing.
Among the problems with this statement is McCoy's belief that sobriety leads to being conquered. Perhaps McCoy meant that in space warfare once your space fleet was defeated and the enemy was poised to attack your planet, immediate surrender was the only option and only drunk persons would choose to fight.
Anyway, McCoy believed that Vulcan had been conquered at least once, maybe yesterday, maybe millions of years ago.
But in "The Immunity Syndrome" Spock sensed the deaths of 400 Vulcans on the starship Intrepid many light years away:
SPOCK: Captain, the Intrepid would have done all these things too, and yet they were destroyed.
KIRK: Well, they may not have done all of these things. You just pointed out how illogical this situation is.
SPOCK: True. It is also true they never knew what was killing them. Their logic would not have permitted them to believe they were being killed.
SPOCK: Vulcan has not been conquered within its collective memory. The memory goes back so far that no Vulcan can conceive of a conqueror. I knew the ship was lost because I sensed it.
KIRK: What was it you sensed?
SPOCK: The touch of death.
KIRK: And what do you think they felt?
This dialog has many puzzles, such as seeming to equate conquest with death. I may note that my country, the USA, has never been conquered, and that I have never died, not even once, and yet I can imagine being conquered and being killed.
Anyway, this shows that Vulcan has never been conquered since the collective memory of Vulcan began, and thus either Vulcan was conquered once or more times before the beginning of the collective memory of Vulcan, or else has never been conquered. And possibly McCoy and Spock have different definitions of being conquered. Maybe McCoy thinks that if the Vulcans acted like "cheese-eating surrender monkeys" - also known as rational people - and surrendered without a fight when faced with overwhelming odds they were conquered, while Spock limits being conquered to fighting against hopeless odds to the bitter end and being crushed and slaughtered.
In "Balance of Terror" it is discovered that the never before seen Romulans look like Vulcans.
SPOCK: I agree. Attack.
KIRK: Are you suggesting we fight to prevent a fight?
MCCOY: Based on what? Memories of a war over a century ago? On theories about a people we've never even met face to face?
STILES: We know what they look like.
SPOCK: Yes, indeed we do, Mister Stiles. And if Romulans are an offshoot of my Vulcan blood, and I think this likely, then attack becomes even more imperative.
MCCOY: War is never imperative, Mister Spock.
SPOCK: It is for them, Doctor. Vulcan, like Earth, had its aggressive colonising period. Savage, even by Earth standards. And if Romulans retain this martial philosophy, then weakness is something we dare not show.
Obviously Spock could have meant Earth's age of discovery and later age of colonialism when talking about Earth's "aggressive colonizing period". However, if Spock believed the Romulans living in a star system far from Vulcan were descended from Vulcans in Vulcan's "aggressive colonizing period", Spock must have believed that Vulcan had interstellar travel during some part of Vulcan's "aggressive colonizing period".
Thus it is possible that Spock believed that Earth's "aggressive colonizing period" lasted past the 20th century and into the early stages of Earth's interstellar travel, that Earthmen might have acted like Romulans or Klingons in early phases of Earth's interstellar travel. Later Star Trek productions seem to have made that possibility more and more unlikely.
In any case, Spock believed that Vulcan's "aggressive colonizing period" lasted into the era of Vulcan's interstellar travel. Vulcans would have colonized planets suitable for Vulcans and conquered other intelligent species they discovered.
According to "Amok Time":
KIRK: It's lovely. I wish the breeze were cooler.
MCCOY: Yeah. Hot as Vulcan. Now I understand what that phrase means.
KIRK: The atmosphere is thinner than Earth.
KIRK: And you said Spock might not be able to handle him. If I can knock Spock out without really hurting him
MCCOY: In this climate? If the heat doesn't get you, the thin air will. You can't do it!
MCCOY: Is this Vulcan chivalry? The air's too hot and thin for Kirk. He's not used to it.
In "The Deadly Years":
SPOCK: I have a question for the doctor. (Kirk leaves) Doctor, the ship's temperature is increasingly uncomfortable for me. I've adjusted the environment in my quarters to one hundred twenty five degrees, which is at least tolerable. However, I___
Clearly normal Earth temperatures combined with thicker air would make Earth conditions deadly for Vulcan children and elderly Vulcans, who would lack the ability of strong adult Vulcans to survive in Earth's environment. So the Vulcans wouldn't have colonized Earth, sticking to colonizing more Vulcan-like planets, but may have captured primitive cavemen and taken them to other Earthlike worlds to breed and train as workers in the service of Vulcan, perhaps helping to explain the many alien planets with natives that looked like humans.
So why haven't the Vulcans told everyone that the aggressive unseen aliens coming from the Vulcan colonized system 618-396, or whatever the Vulcans called it, should be descended from Vulcan colonists long ago? Because the hypothetical Vulcan Space Empire fell, probably in some bloody wars, and civilization on it's planets was destroyed. All record of the history of the hypothetical Vulcan Space Empire was lost on Vulcan, Romulus, and all other planets in the Empire. And ruins of civilization were gradually destroyed over thousands and tens of thousands of years on planets with atmospheres, tectonic activity, and weather.
Many, Many thousands of years later, Vulcans built a new civilization on Vulcan. Exploring their solar system, and later other stars, they found remains of space vehicles, space stations, and domed colonies on airless worlds, surviving due to the lack of weather, and learned to read the ancient Vulcan writing and learn something of the history of the hypothetical ancient Vulcan Space Empire. But obviously not the coordinates of every star system that had been settled by Vulcans.
And civilization was rebuilt on Romulus, and probably other planets that had been settled by Vulcans or with non Vulcan natives who had been ruled by Vulcans, and eventually the Romulans began to travel in interstellar space and conquer other planets.
That is basically what can be deduced from "Balance of Terror".
In "Court Martial", in a club on Starbase 11:
KIRK: Timothy, I haven't seen you since the Vulcanian expedition. (no reply) Well, I see our graduating class from the Academy is well represented. Corrigan. Teller. How you doing, Mike?
This certainly sounds like Kirk and Timothy were in an expedition to Vulcan. But in their lifetimes just decades before TOS, wouldn't it be more like a trip to Vulcan? Vulcan would hardly seem like an expedition destination in Kirk's lifetime.
Maybe Kirk and Timothy were the only two humans in the crew of a Vulcanian ship when it made a voyage or expedition to some distant star system.
Or maybe in Kirk and Timothy were in the crew of a ship named Vulcanian, named after the planet Vulcan or maybe the ship's name was a synonym for "Volcanic".
Or maybe Starfleet really had a Vulcanian expedition to Vulcan in Kirk's lifetime which would be a little understood event in Vulcanian history.
In "Return to Tomorrow Sargon tells a little of the history of his planet:
KIRK: That's twice you've referred to us as my children.
SARGON: Because it is possible you are our descendants, Captain Kirk. Six thousand centuries ago, our vessels were colonising this galaxy, just as your own starships have now begun to explore that vastness. As you now leave your own seed on distant planets, so we left our seed behind us. Perhaps your own legends of an Adam and an Eve were two of our travellers.
MULHALL: Our beliefs and our studies indicate that life on our planet, Earth, evolved independently.
SPOCK: That would tend, however, to explain certain elements of Vulcan prehistory.
SARGON: In either case, I do not know. It was so long ago, and the records of our travels were lost in the cataclysm which we loosened upon ourselves.
KIRK: A war?
SARGON: A struggle for such goals and the unleashing of such power that you could not comprehend.
KIRK: Then perhaps your intelligence wasn't so great, Sargon. We faced a similar crisis in our early nuclear age. We found the wisdom not to destroy ourselves.
SARGON: And we survived our primitive nuclear era, my son. But there comes to all races an ultimate crisis which you have yet to face.
KIRK: I don't understand.
SARGON: One day our minds became so powerful, we dared think of ourselves as gods.
If Vulcans are descended from Sargon's people, which is not certain, Vulcan history began 600,000 years ago or later, sometime after Sargon's people began to colonize other worlds.
Earlier, Sargon's planet was described as:
SPOCK: Class M planet, Captain.
KIRK: Close to Earth conditions.
SPOCK: With two very important exceptions. It's much older than Earth, and about a half million years ago, its atmosphere was totally ripped away by some sort of cataclysm. The planet has evidently been dead since then. Sensors detect no life of any kin
So Sargon's planet apparently had interstellar travel for about 100,000 years before the final cataclysm about 500,000 years ago.
Obviously, all the colony planets of Sargon's people were also devastated in that final war, with either everyone being killed or else civilization being destroyed and the few survivors reduced to being hunter gatherers. Otherwise one of those colony planets would have sent starships to explore the remains of the home world and would have found Sargon countless thousands of years before Kirk.
So if Vulcan was colonized by Sargon's planet Vulcan's separate history might have begun 500,000 years ago with a few survivors of the war that wiped out Sargon's planet. And if the Vulcans aren't descended from Sargon's people there is no evidence of how old the Vulcan species is.
And it is possible that the hypothetical Vulcan Space Empire was founded by relatively primitive Vulcans who learned how to build interstellar space ships from visiting aliens who they might have captured and enslaved, and then invaded the alien's home planet, conquered it and made it part of their emppire.
In "Let That Be Your Last Battlefield":
SPOCK: Commissioner, perhaps the experience of my own planet Vulcan may set an example of some value to you. Vulcan was in danger of being destroyed by the same conditions and characteristics which threaten to destroy Cheron. We were once a people like yourselves, wildly emotional, often committed to irrationally opposing points of view, leading, of course, to death and destruction. Only the discipline of logic saved my planet from extinction.
In "The Savage Curtain" the image of Surak, founder of Vulcan logic, says:
SURAK: In my time on Vulcan, we also faced these same alternatives. We'd suffered devastating wars which nearly destroyed our planet. Another was about to begin. We were torn. But out of our suffering some of us found the discipline to act. We sent emissaries to our opponents to propose peace. The first were killed, but others followed. Ultimately we achieved peace, which has lasted since then.
This makes it seem like Vulcans were confined to Vulcan at the time of Surak, and had atomic bombs and missiles, or worse weapons, at the time.
In "How Sharper than a Serpent's Tooth" they meet the alien Kulkulkan who inspired many Earth legends:
MCCOY: Spock, I wouldn't suppose that Vulcan has legends like those?
SPOCK: Not legends, Doctor. Fact. Vulcan was visited by alien beings. They left much wiser.
Spock apparently is referring to visits to Vulcan after the reforms of Surak. Presumably the Vulcans taught the aliens about Vulcan logic and Surak's philosophy, making the aliens much wiser. And maybe the Vulcans learned the technology of interstellar travel from those aliens, which would make the Vulcans and the aliens "guide civiliations" to teach other.
And if Vulcans have lived on Vulcan for hundreds of thousands of years, as "Return to Tomorrow" implied might be the case, Vulcan might have been visited many times by various space traveling aliens during that period, and some of them might have interacted with Vulcans and helped them to advance, thus being "Guide civiliations" to Vulcan civilization.