It's good to try different times and find the best routines for you. It may also change during the season or period of your life. I loved the feeling of waking up at 4 a.m and walking around the sleeping city.
However, I've noticed that even though I'm an introvert, if I want to have a social life, 5.30 works best. The city is still silent for having a morning walk, and you have time for the excellent morning routine before the hustle begins. Try, explore, and find the best one for you.