So would you call with your entire range or something? And I guess only 3bet until you have build up more 3bet dynamic?
In the SB, I'm calling AK, QQ+ 100% of the time because I think there's more value vs. BB squeezes than vs UTG's raise/call and 4bet/call range as a standard, because either the UTG will raise/call or 4bet/call wider vs the squeeze than he will vs the cold 3bet and both players will perceive your range as capped to AQ, JJ- when you either 4bet the BB after the UTG folds, 5bet all in after the UTG 4bets or over call to "set mine."
FWIW, this is an empirical observation at 200nl, 3bet/5betting vs UTG/MP from the blinds with AK, QQ- is a net loss to the rake.
In the BB, calling AK, QQ+ doesn't have the same value as in the SB without the squeeze dynamic, however in the BB you're calling 88-22 to set mine now so you're adding AK, QQ+ to balance the addition of weaker hands in your range. There may be an argument for only calling AK, QQ and 3betting KK+ if your opponent's UTG range is wide enough to 3bet bluff as well, where getting KK+ in vs AK, QQ+ is +EV as well as getting the opponent to fold XX when you bluf with KQo, AJo, Axs, maybe Kxs type hands within a reasonable, albeit exploitative, frequency.
If I were disregarding balance and exploiting SSNL, I'd just flat my premiums and 3bet bluff 100% vs a wide enough UTG/MP range and trust a ~3% 3bet range of 100% bluffs would go unchallenged by anything less than a 4bet of AK, QQ+ and a raise/call of AQs, JJ with AQo, AJs, KQs, TT pushing it vs a spewtard or 99- vs a set miner laying out dead money for Cbets.
As a consequence, whenever the opponent 3bets you in UTG/MP from the blinds, 4bet/calling is -EV compared to raise/calling with AK, QQ.
None of this applies with a caller, your perceived range for squeezing vs the UTG is significantly looser than it is for cold 3betting.
Obviously you adjust as the game progresses as you see fit (or need to) but getting dealt QQ in the blinds vs an UTG raise from a regular and 3betting him without history is as good as lighting money on fire IMO.