Sorry i dont know if i understand the question right.
I guess you looking for the fireplace/chimney to climp up, in the present, after you got it repaired, in the past, and use another time gate on the higher floor to get back to the past.
how do you access the other time gate it's over a drop you can't pass
You can interact with the pile of wood one floor above it to drop it down and make a bridge.
Hope that helps^^
how do you enter the room with the wood i can't seem to find a key
The key is in the past in the storage room in the base. Just talk to the guard blocking the entrance to trogger a cutscene.
thank you