I, like you, am guilty of this. I have different ways to handling it, some are combinable, but not all.
The main purpose of all of this is to make the game more enjoyable to your players, because the problem with GMPCs is that it tends to ruin the fun for the players. So you have to ask yourself (and/or your players) what specifics are to be avoided. I had groups that enjoyed being the guys that hang around Mr. Coolguy and listen to the story and I had groups that shot him dead.
If the character stays with the group and is important to the story, tell your players directly that you are going to play a PC with them.
So, now my advicelist:
He must be coherent to the rules of the game. He may be twenty levels above the PCs (or whatever concept for power exists) but he still is within game mechanics and thus beatable by game mechanics. If he is injured write that down on his sheet. Don't go over it like 'that scratch wouldn't bother him'.
Make him super-whatever but gamewise unimportant. The one who gives the group their adventure may come over like a young god, yet to the actual story it doesn't matter at all. (The Johnson)
Give him some social problems, small, shy, geeky, clumsy. He actually needs the PCs because he just can't handle the world despite being awesome otherwise.
Handle him like you would have your PC handled by another GM, that makes him more like a character and less like a plot device.
Let him leave the group for prolonged periods and return after that. So there should be multiple sessions without him, then he returns only to leave again after that.
If you want him important to the story let the players try to recruit him into their team (and succeed) rather than forcing them to take someone with them they don't like.
D&D5 - The bad guy should not be surprised.
PHB, p.189 - Surprise
A band of adventurers sneaks up on a bandit camp, springing from the trees to attack them. A gelatinous cube glides down a dungeon passage, unnoticed by the adventurers until the cube engulfs one of them. In these situations, one side of the battle gains surprise over the other.
The DM determines who might be surprised. If neither side tries to be stealthy, they automatically notice each other. Otherwise, the DM compares the Dexterity (Stealth) checks of anyone hiding with the passive Wisdom (Perception) score of each creature on the opposing side. Any character or monster that doesn’t notice a threat is surprised at the start of the encounter.
As @KorvinStarmast stated, there is no such thing as a surprise round in 5E. A surprised character is simply not able to move, take an action or a reaction on his first turn of the combat.
In your situation, the bad guy is clearly facing the characters when doing his speech, so unless he is fanatically speaking to his hidden god of evil somewhere in the skies, he will see the character doing his move and won't be surprised.
If the party was speaking with a friendly noble NPC, for example, and a PC decided to attack suddenly, the NPC should be surprised, because he wasn't aware of the threat. When a BBEG faces a party of characters, it seems obvious that they are antagonists/foes/enemies and that each side is a threat to the other. In the end, it is the definition of threat that makes a difference.
Also, giving the player a round during which he alone can act might lead others to abuse this mechanic.
Best Answer
That depends on what you mean by villain
If you meant the BBEG (Big Bad Evil Guy - the main Villain of the Campaign), I will start with some frame challenging:
You don't.
A BBEG that is going to be defeated by level 1 characters is probably underwhelming. That's an animated armor or bugbear level of threat. Anything your players can beat with just their lvl 1 features and spells probably isn't going to be a Villain level of enemy.
So, just make usual encounters. If you don't know how, it's explained on p. 81 of DMG or p. 56 of the free DM's Basic Rules PDF. From my experience the difficulties are easier than what they say - deadly usually means having to spend some resources (class features and spell slots), but unless your players are unlucky, deadly shouldn't be actually deadly.
Let them get some levels. By level 3 to 5 they might be able to defeat something that actually could be called a BBEG.
However, you present the campaign villain early on1
In the comments, goodguy5 suggested to introduce the Villain without combat. He gave two examples that you can read below, but I'll use the one from an official adventure - Strahd von Zarovich from CoS.
He is introduced almost as soon as the adventure starts, but he is only supposed to be fought by level 10+. He shows up in person some times, either to scare adventurers or to play them (or without them being the reason he shows up). If they engage combat against Strahd, he will charm them, make them fight each other and might try to turn one into a vampire, but he will not just kill them, because that would be unfun for him.
If you mean just a boss, not the big one
You can get some monsters, as the Bugbear mentioned, and give them some lore. If you can afford it, Lost Mines of Phandelver does exactly that and might teach you some things (the Starter Set is amazing for that).
Make the Animated Armor a guardian or a cursed soul. Make the Dryad corrupted by the destruction of a forest. Anyway, take CR 1 (at max CR 2) monsters and give them a background, a motivation, a story. That should be enough for 1st lvl.
If you want to create a new monster, p. 273 from DMG explains how to do it and calculate the CR in order to keep it balanced.
TL;DR:
The DMG gives clear guidelines as to what is a balanced encounter to any party size and levels. You probably shouldn't have a BBEG that is defeatable by 1st level characters, but a "Boss" can be made taking usual CR1 monsters and giving them lore.
Quick note about similar-to-PC villains
AFAIK, there is no guideline to what CR a PC would be (they use CR = PC when needed, but this is just gross, if a CR1 monster is supposed to be a decent encounter against FOUR level 1 PCs, there is no way a level 1 PC is equivalent to a CR 1 monster). Without experience, you probably shouldn't try to make a PC-like villain, as it is easy to make it overpowered or underpowered.
1 Related: How do I present an unbeatable encounter without frustrating my players? - Years later, I found out that, sometimes, presenting a strong villain early on (specifically Strahd, as in my answer here) may lead to player frustration because they may feel powerless. Still, I would like to mention that I have done it several times before and this was my first time getting this feedback, so YMMV, and I believe this answer is still useful.