There’s different traditions of when is the right time to recite tikkun chatzot. The Baal Sefer Hamidos states the correct the time as 6 hours after nightfall, whenever nightfall happens, and not necessarily in the middle of the night. (Others go for the middle of the night). If a person finds it difficult to get up then, they would be advised by the same author to start it later such as at 3am. It would seem that if one did not recite it by daybreak then it would be too late. Kol hakavod for wanting to do tikkun chatzot, the seforim explain that all the kedusha of putting on tefillin comes from the avoda one does from chatzot onwards.
a yerushalmi yid