I run first thing in the morning because (a) I just can't stand to run with anything in my stomach, and (b) it's the only time I can be sure of actually having the time to myself to do it.
On a typical work day (pre-COVID work-at-home!) I would get up about 4:40 am, start the coffeemaker, get dressed to run, gulp down half a cup of coffee, use the bathroom (hopefully both #1 and #2), and hit the road about 5:00 am. Typically I run for about 90 minutes. On the rare occasions when I can't make #2, I run several small loops so that if caught by surprise I can get back home fairly quickly and take care of it.
On weekend I usually sleep about 45 min later and give myself an extra 15 minutes or so to wake up and warm up, so I start more like 6 am. Only in the middle of summer, when it quickly gets too hot, do I start my weekend runs at 5 am.
This has been working for me for about 35 years. I do need a little more time to warm up in the morning at age 61 than I did at age 30.
And even when doing long marathon training runs, I never eat before running. For runs longer than about 16 miles I carry a couple of gels and down them during the run.