The Jedi attempt on his life left him "scarred and deformed". However, has he always been this way since becoming a Sith Lord and being physically twisted by the dark side, such that the normal-looking facade we see during the prequels is a product of Sith sorcery? Or did he sacrifice his original, very real good looks to seduce Anakin to the dark side?
Sidious' face apparently looked that way before getting hit by lightning in canon, and definitely did in Legends.
In the 2017 Darth Maul comic series, which takes place before Episode I, Maul has a conversation with Darth Sidious, who appears to already look like the Emperor post-duel:
Later in the series, they talk again, and this time Sidious has visibly yellow eyes:
So there is canon evidence that Sidious looked that way already, and the comic seems to imply that this is Sidious' "true" face that he only shows to Darth Maul. As far as I know, this is all we really have to go on within current canon (aside from the ROTS novelization), since in The Phantom Menace what we see of his Sidious face looks relatively normal.
In the Revenge of the Sith novelization, Palpatine examines his face after Mace Windu has been hurled out the window (page 361, emphasis mine):
Palpatine examined the damage to his face in a broad expanse of wall mirror. Anakin couldn't tell if his expression might be revulsion, or if this were merely the new shape of his features. Palpatine lifted one tentative hand to the misshapen horror that he now saw in the mirror, then simply shrugged.
"And so the mask becomes the man," he sighed with a hint of philosophical melancholy. "I shall miss the face of Palpatine, I think; but for our purpose, the face of Sidious will serve. Yes, it will serve."
This seems to heavily imply that this new face, "the face of Sidious", is really his true face.
In Clone Wars, his face as Sidious seems to have crooked teeth and more lines, where his face as Chancellor Palpatine does not:
Also, the ambiguously-EU-canon comic Sithisis is about Palpatine performing some sort of ritual, during which he looks like the Emperor/Sidious:
Finally, if Wizards' Star Wars Roleplaying Game is an acceptable EU source:
Palpatine, who has delved extensively into Sith lore, was using an almost-forgotten technique to hide his true self.
This explanation cites two Star Wars Insider answers, and comes up with a Sith Alchemy ability that masks the user's true appearance (emphasis mine).
[The] real Palpatine is the one who bursts forth at a calculated moment . . . That is when the true person comes out, letting the evil fully manifest itself. The Emperor . . . looks like he does because he's very old and very evil -- it is what he always looked like. [Star Wars Insider 82 (page 58)]
[It’s] the intensity of reflected lightning and the channeling of such raw dark side power that are the catalysts for Palpatine’s transformation. Perhaps the face that boils up to the surface is shaped by his dark side corruption, but the lightning is definitely the cause. [Star Wars Insider 83 (page 32)]
Just as Sith alchemical techniques can be used to make a subject appear more horrific, they can be used to conceal its true appearance. [...] However, the mask can be dispelled by dark side energy: If the subject takes damage from a dark side Force skill, the subject must make a Fortitude save (DC 5 + damage dealt) or the mask is removed and the subject’s true face reappears.
Yes, he was always "scarred and deformed". Put in quotation marks because he was neither: That's his true form. Every time we see Sidious in The Phantom Menace, Attack of the Clones, and The Clone Wars, he's in his "scarred" form. The reason Ian didn't wear any makeup was because he was old enough and the hood already covered his face enough, plus make-up is very time-consuming (I read somewhere that back in Return of the Jedi, it took 5 hours for Ian to finish the makeup). Not to mention the few times that Sidious appeared outside of holograms in The Phantom Menace and Attack of the Clones, he was always in very dark places. Sidious' face being "scarred" all along is also why he could play both sides without being caught: Even if the Jedi saw him, they wouldn't be able to tell that he's Chancellor Palpatine. Look at Palpatine's face in Return of the Jedi:
Then imagine only his mouth being shown, and he wouldn't look different from Sidious in The Phantom Menace:
Put his scene with Maul in The Phantom Menace and his scene with Vader in Revenge of the Sith side-by-side and you would see the resemblance:
While Sidious may look more pale in the latter screenshot, it's because of the light. There are times that we see him with skin that resembles humans':
Notice how Ian wore makeup on his hands when playing the Emperor in Return of the Jedi:
Yet when playing the "scarred" Sidious in Revenge of the Sith, he clearly didn't wear any, save for barely-noticeable fingernails:
Let's compare Sidious' post-"disfigurement" voice to his pre-"disfigurement" one. This is him in The Phantom Menace:
As you can see, Sidious' voice remained the same before and after his "disfigurement", because it's his real voice. Plus one thing is certain: Due to Sidious being a Sith, whenever we see him in The Phantom Menace, Attack of the Clones and The Clone Wars, his eyes are yellow even though we only barely see them in The Clone Wars. If Sidious could mask his eyes, I don't see why he couldn't mask his face. For further evidence, here's Sidious in The Clone Wars:
Look at his face closely and you would see the "disfigurement", especially when comparing it to a vision of the "disfigured" Emperor in the episode Ghosts of Mortis:
And here's Palpatine in the Special Edition of The Empire Strikes Back:
Imagine his face except for his mouth and neck being obscured and you would see the resemblance to Sidious in The Phantom Menace. Lastly, Ian explicitly stated in an interview that Sidious was indeed "disfigured" all along:
"[Lucas] said this casually, 'You should think of Palpatine's eyes as contact lenses...' So there's Palpatine's eyes and my eyes and that was very interesting. So, in fact, his face, which is the same as mine, was the unreal aspect. My own face was the mask. And then when I get into the mask, that is the evil person - that's the real face." —Empire, "The Emperor Speaks: Ian McDiarmid Interview"