On his first entry to the castle, he’s missing two clues:
- The word “BIRD” scribbled in the sand of the teleporter room
- The passage of the stars
So we need to work out a course of action without either clue, the latter of which will only become apparent in decades to come.
By the time we arrive in the diamond room, here’s what we know:
- The Veil is temporarily slowed by confessions, and these confessions drive the layout of the castle.
- The clues are supposed to lead the Doctor to Room 12; to the insurmountable wall of diamond.
- All the rooms in the castle reset to just before the Doctor’s arrival.
- The Doctor knows more about the Hybrid than he’s letting on.
It’s not a stretch to suppose the point of this castle is to get information about the Hybrid. Continue backing the Doctor into corners, he confesses to buy a bit more time, and eventually you learn what you need to know, right?
The two previous dead ends have resulted in confessions, but clearly they’ve been unsatisfactory to the powers-that-be. The Doctor works out how this is supposed to go: trapped with no way out, facing down the Veil, he gives up information about the Hybrid. His life is spared, and somebody has their secret.
(Note: if the Doctor sells out, he’d die anyway. This is standard villain behaviour.)
He also works out that there’s something beyond the wall. If he can get through it, there’s an alternative exit route.
There’s enough here to work out what needs to happen next. Chip away at the wall, over thousands of copies, and eventually you’ll get through. (He doesn’t know if this will work, but he’s running out of options.)
The word “BIRD” is a nudge in this direction. He’ll work it out faster on subsequent iterations – perhaps earning him an extra punch or two – but it’s not absolutely necessary to work it out. The passage of the stars is a similarly useful but not necessary clue.