Well you're right there's infinite variations of algos that all can legitimately be called hill-climb. It's about as generic as the term "curve fitting".

I just mean with the known complexity and nature of Game of Life, trying to guess things based on an objective function, when going back in time, seems no more efficient than trying to guess coin flips, based on prior flips. There's probably some Logic Theorem (sorry I don't know it) that describes why objective functions cannot be used to help solve the backwards Game of Life problem.

It's a complexity problem like which butterfly "caused" a tornado, or which initial clumping of rocks "caused" a black hole, because there are infinite numbers of solutions. Like how many initial GoL boards are there that result in a particular final state? I say for any final state there will be infinite possible starting states that can lead up to it.