Unlocked iPhone 12 from Apple

My wife currently has a line with AT&T. I don't, my line is with another carrier through work.

If I buy an 'unlocked' iPhone 12 directly from Apple and give it to my wife as a gift, will she be able to set it up with AT&T and easily replace her old iPhone? I'll be holding this for over the two-week return policy by Apple, so I need to be sure. When I try to buy an iPhone 12 connected with AT&T, they ask for AT&T account information or require me to set up a new account. So my only choice as I see it is to buy an unlocked phone or look for another gift. So again, if I buy an 'unlocked' iPhone 12 directly from Apple and give it to my wife as a gift, will she be able to set it up with AT&T replacing her old iPhone?