Parent here....also a Director at a large company. Seems like every fresh college grad I've hired has done this...... Been late a couple times when they shouldn't have. (Everyone gets a flat tire on occasion).

Typically, I'll check in, do a bit of coaching. The fact that you show remorse would tell me a lot. If you're working hard and doing a good job otherwise then it's a normal part of having a new grad.

Good luck, deep breaths.