I'm not keen on playing the game of everything only exists in the mind since common sense says it is false. However....
God and Thought experiments
Well, I thought about this and come to the following conclusions.
1. If god is an omni god, though experiments would be useless as he would know the answer and the question at the same time so would not have any thinking to do at all.
2. If god is one of those changeless gods some hymns talk about, then he could not do anything - think or act - as that would involve change on his part.
3. Well, supposing he could do a thought experiment - say what you it be like if I killed off mankind and started again? To do this, he would not be omniscient (see 1 above) and that would run the risk that he would get the results wrong and then act on them - you know, like give some crazy design for a boat that would break up in a storm to a guy he wanted to save all the animals. Uh, oh, that YHWH did that, didn't he.... ah, well, maybe an non-omniscient god isn't such a good idea anyway.