W.T.
We went about month waking up at 4am on the dot! Ugh, it sucked. 5am I can handle, but 4am is rough.
I would just keep doing what you are doing, minus the crying....personally I don't believe in cry it out.
This too shall pass I promise. 1 year olds are just at a great phase of life. Things are happening so quickly to them. Walking, learning, teething that the world is a great place to be awake.
Can you put him in bed with you and doze? Can you put a mattress in his room and doze with him or doze while he is doing his own thing?
It really won't last long. Just hang in!