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In Deathly Hallows, during Snape's memories, right after Voldemort's ‘death’ at the Potters’ house, Dumbledore states, "The Dark Lord will return, and Harry Potter will be in terrible danger when he does".
How does Dumbledore know Voldemort will return?
Is Dumbledore aware of the Horcruxes?
Does he know about the second prophecy of Professor Trelawney (which isn't revealed until 15 years later)?
By the end of Harry Potter and the Chamber of Secrets, Dumbledore had indisputable evidence that Voldemort had created at least on Horcrux:
Dumbledore paused for a moment, marshaling his thoughts, and then said, “Four years ago, I received what I considered certain proof that Voldemort had split his soul.”
“Where?” asked Harry “How?”
“You handed it to me, Harry,” said Dumbledore. “The diary, Riddle’s diary, the one giving instructions on how to reopen the Chamber of Secrets.”
—Harry Potter and the Half-Blood Prince
That he called this "proof" suggests that he had harbored suspicions for a long time.
After all, he had seen the great alteration in Voldemort's physical appearance when the latter came to interview for a position as Defense Against the Dark Arts teacher. Dumbledore was well-acquainted with Dark Magic; it was undoubtedly he who had removed the books on Horcruxes from the Hogwarts library, and he had probably read them. He may well have suspected what those changes were due to, particularly with his knowledge of Voldemort's obsession with immortality.
If Dumbledore thought that Voldemort had Horcruxes (or some other means of immortality), he would certainly have expected him to return.
Dumbledore wasn’t the only one who thought the Dark Lord wasn’t dead - when he killed the Potters, most wizards thought he’d lost his powers but not actually died.
“Professor McGonagall’s voice trembled as she went on. ‘That’s not all. They’re saying he tried to kill the Potters’ son, Harry. But – he couldn’t. He couldn’t kill that little boy. No one knows why, or how, but they’re saying that when he couldn’t kill Harry Potter, Voldemort’s power somehow broke – and that’s why he’s gone.”
- Harry Potter and the Philosopher's Stone, Chapter 1 (The Boy who Lived)
Knowing that, Dumbledore likely thought the Dark Lord would return was inevitable - he’d lost his powers, not his life, so he’d be trying to get them back, and Dumbledore didn’t underestimate him. Whether Dumbledore had realized that the Dark Lord might have survived it because of Horcruxes or not, he knew the Dark Lord wasn’t dead so it was possible, even likely, that he would return.
Though most wizards suspected that the Dark Lord wasn’t dead, it’s likely that Dumbledore already had his suspicions about his methods used to enable him to survive it by then.
“I have been hoping for this piece of evidence for a very long time,’ said Dumbledore at last. ‘It confirms the theory on which I have been working, it tells me that I am right, and also how very far there is still to go …”
- Harry Potter and the Half-Blood Prince, Chapter 23 (Horcruxes)
He’d certainly suspected what Harry’s scar meant, so it’s very likely he’d suspected the Dark Lord had created Horcruxes then as well - that would explain why the Dark Lord’s soul was fragile enough that a piece of it could break off without him knowing and embed itself in Harry.
“I guessed, fifteen years ago,’ said Dumbledore, ‘when I saw the scar on your forehead, what it might mean. I guessed that it might be the sign of a connection forged between you and Voldemort.”
- Harry Potter and the Order of the Phoenix, Chapter 37 (The Lost Prophecy)
This would make Dumbledore even more sure the Dark Lord would return than anyone else - having Horcruxes would mean the Dark Lord couldn’t die unless they were all destroyed, so there was no hoping he’d simply die before he finds any way to regain his powers.
My opinion: Dumbledore was probably pretty darn sure any Dark Wizard of Voldemort's stature would have created a horcrux somewhere. The concern about multiple horcruxes only came about after Chamber of Secrets, when Dumbledore noted that the Diary horcrux was treated so casually. But Dumbledore believed with all that Voldemort was up to during the First Wizarding War, it was unlikely he would have forgotten to create a horcrux. Also, the attack on the Longbottoms would have indicated to Dumbledore Voldemort's followers believed Voldemort had a plan to return. The Lestranges and Barty Crouch, Jr. would not have bothered torturing the Longbottoms if they believed Voldemort were truly gone.
In addition to Adamant's Answer. There is a section in Short Stories from Hogwarts of Power, Politics and Pesky Poltergeists which details why Dumbledore had suspicions about what Lord Voldemort had achieved during the first wizarding war.
Dumbledore already had suspicions as there was a rumour he had made himself invincible. Then after the defeat of Lord Voldemort, his suspicions were raised even move given Professor Slughorns guilt over what he has discussed with Tom Riddle at school about Horcruxes. When Dumbledore tries to question him over this Slughorn retired from the school.
When the wizarding world fell into war, and rumours swirled that Voldemort had, somehow, made himself immortal, Slughorn was sure that it was he who had made Voldemort invincible, by teaching him about Horcruxes (this guilt was misplaced, as Riddle already knew how to make a Horcrux, and had feigned innocence in order to find out what might happen if a wizard made more than one). Slughorn became ill with guilt and fright. Albus Dumbledore, now Headmaster, treated his colleague with particular kindness at this time, which had the paradoxical effect of increasing Slughorn’s guilt, reinforcing his determination never to tell a living soul what a dreadful mistake he had made.
Lord Voldemort made no attempt to seize Hogwarts on his first ascent to power. Slughorn believed, correctly, that he was safest remaining in his post rather than risking the outside world while Voldemort was at large. When Voldemort met his match upon attacking the infant Harry Potter, Slughorn was even more jubilant than most of the wizarding population. If Voldemort had been killed, Slughorn reasoned, then he could not have made a Horcrux, which meant that he, Slughorn, was innocent after all. It was Slughorn’s extremity of relief, and the disjointed phrases he let fall in the first rush of emotion after hearing of Voldemort’s defeat, that first alerted Dumbledore to the possibility that Slughorn had shared Dark secrets with Tom Riddle. Dumbledore’s gentle attempts to question Slughorn, however, caused him to clam up. A few days later, Slughorn (who had now completed a half century of service to the school) tendered his resignation.
