QQ 6max

Hi, blicax,
Disclaimer: I am NOT a coach!;

In a cash game, I really don't see much hope in avoiding this.
If your opponent is an uber-nit maybe, but even if he opens 5% UTG you are ahead of his range.
You would need a decent sample to even know what his UTG range is, though. With less that 75 UTG hands (roughly 450 hands total) you're just guessing anyway.

       Equity     Win     Tie
MP2    43.98%  42.80%   1.18% { TT+, AJs+, AQo+ }
BU     56.02%  54.84%   1.18% { QQ }

Some things that MIGHT work in some situations I'm not saying I recommend any of these, but they are alternative lines vs some player types.
 3Bet bigger pre, fold to shove. If your 3Bet is big enough to force him to commit his stack, you have more fold equity, and his shove is much less likely a bluff, so you can fold and save money. This line might also be effective against players that are sensitive to bet sizing -- but again, you have to know that.
 flat pre. This is good vs aggro players that can open raise pre and bet/call flops with stuff like Ax when they hit their weak top pair, and you then mop up with your overpair.
 Call the flop. This is a fairly wet board, and you might be able to represent a straight or flush if such a hand becomes believable -- as on the turn here. This only works if you flat-called pre though, because no-one would believe that you'd 3Bet UTG with TJo, for example.

Maybe others have some alternate suggestions.

In any case, he is almost never folding AA, and pretty much all possible lines lead to the same end.

Best of luck,
VS

No stats on villain? His 4bet is huge.

flat call QQ pre vs UTG without reads = avoid

As it is 5player table it is debatable whether it id UTG or MP.

I think that, if we decided to 3bet, we should rather shove than call a 4bet. He is never bluffing there, but can still have hands like AK and JJ and hand like AK might check/fold the flop if doesn't hit. Also, it's weird to call and see A or K on the turn. I'm not sure what would be the best play with QQ in this situation, both if he bets or check. I believe we should fold if he bets and check back if checks.

5bet or fold pre. Personally I would never fold QQ 6max against an unknown after 3 betting, too tight for 6max imo.