Like removing the doorframe and putting in your own new door that doesn't lock, then walking inside

What if picking the lock damages the lock?

Yeah. It might not be a search, but it's something, and the logical question is to ask under what authority can that be done.

is when they got the warrant

I guess that is the question. If the police are confident that they will have a warrant in 30 minutes, can they have a locksmith unlock the door while they wait?

I would say no, because the whole point of the warrant is to remove the police's judgement from the equation. If they're taking action based on their expectation that they'll get it, that's kind of an end-run around the stated purpose.