Urgot's Skill Max Order: W → E → Q
Urgot's E range: 450 units, which is 75 less than your AA range
Urgot's W range: 490 units, which is 35 less than your AA range
Matchup Tip: An advanced tip is to use E when Urgot is not expecting it aggresively, and if you do this, Instantly AA-after you land to consume the harrier proc, then run away in a quick combo. This will bait Urgot to use his E towards you, but his E is a 0.45 cast time with only 450 Range while your E pushes you back 525 units. He will miss his E every time, so this is great to bait out his E in lane and put him in a bad spot. Do this only level 3 onwards when you have points in W to get MS from its passive.
Level 1: Do not use your E level 1 against Urgot. Most Urgots, if not all, start E level 1 and will flip you mid E, which will kill you. If he E's you, vault right after and then auto him to death.
Level 2: Try to stay at max AA range and you win all trades against Urgot. Be extremely careful about your E useage in this matchup. Side step Qs in lane, and if you land Blind, go in for short trades.
Level 3: You need to Blind urgot during trades because his W will do a lot of damage if he gets in range of you to use it.
Level 6+: Be careful of Urgot's flash engage because he can destroy you if you aren't careful. If he lands flip on you post 6, Instantly vault then side step to avoid his R because he will instantly R you after your vault.
Early game, if Urgot throws a Q at you, trade with your vault and autos and you will win the trade.
Also, you can use your vault to dodge his Q early on, but do this ONLY when you are certain Urgot doesn't have his E leveled up, of course (level 1, and level 2 if you see urgot started W second).
Now, level 3 onwards, this is how you beat urgot. Urgot's E range is 475 after a 0.45 second delay, and vault pushes you back to 525 range.
This trade requires practice, so please limit test with this in normals before trying in ranked, but when you master it, you will consistently beat Urgot in trades.
So, what I like to do is vault Urgot aggressively post level 3 in lane randomly, and then I quickly auto him quick to consume my harrier proc (and also potentially fleet MS proc if your auto is energized), and then I immediately run backwards away from Urgot.
In absolutely every single elo you are in, the enemy Urgot will immediately retaliate with his E because he thinks "oh, Quinn vault down, let me use my E to flip him!" However, his E is a .25 second delay, and your vault with MS allows you to not only out range him, but grant enough MS to consistently outrun his flip every time.
Why is this trade important? Well, Urgot's E is a long cooldown and a big part of his kit, so you can safely trade with him in lane after this, but ALSO, in teamfights, if you do this, Urgot will actually Dash straight into your team for free and will have no escape afterwards.
He relies on flipping you, but if you can bait his flip, then he's legit dashing into your team for free lol.
Post 6 BE READY TO SIDESTEP HIS R! Quinn's in combat MS with fleet and W max is incredible, and It actually gets quite easy to dodge his R with Quinn if you have your reaction speed up.
If he lands it on you, try to vault away before he flips, or if he lands flip, save vault to push yourself away afterwards.