It may not make a huge difference b/c it's all individual & things will effect ppl differently.
But when you first wake up at 6am your body is still in sleep mode even though you're awake. It usally takes anywhere from 1-3hrs b4 the body is completely awake, alert, & full of energy.
Pluse you will be working out on only one meal & your system will be dehydrated after a nights sleep.
I personally find that training at, at least 1pm is better but I can't usually do this b/c of work & a new course I'm taking at work. My training has always been between 4-6pm & no later.
Going to the gym in total takes about 2hrs. You gotta drive there which takes 5-10mins at least, find parking, check in with your card & go into the locker room & put your stuff away, head to your first exercise, stretch & warm up & then train.
Then you got to go back to the locker room, pack your stuff, go to your car & drive home, shower & eat.
All of this takes about 2hrs maybe an hour and a half if you're lucky & fast.
So you also have to have 2hrs available to you.
But for me personally I've found that training in the late afternoon & early evening is much better in general.
You've had 3-4 meals in you providing your body with fuel & nutrients, you've had a chance to drink a few bottles of water & take your vitamin supplements. & your body will be fully awake.
But it's up to you, if you feel better at 6am in the morning, do what you feel is best.