I actually don't really know what villain will be cold 4betting here tbh, I imagine as a standard most people are going to be too tight and value heavy. I do doubt he does have just AK, QQ+ but he probably isn't going to be all that wider.

It might be a good idea to work out if you shove how much villain has to fold for you to profit w/ATC and see if that's ever possibly going to be realistic. Then you can also create an EV calculation for shoving over the top and play about with different ranges to get an idea of what makes this profitable for us to do. A mixture of things like him being tight and calling tight (i.e. AK, QQ+ but only calls w/KK+) him being bluff heavy/value heavy calling tight/loose.