While there is no tried and true set answer to that question, I think the best time to train is when you can do it on a regular and consistent basis. That said, that best time is that period your body normally performs at it’s optimum and that is different for each of us. Whatever period of time that is, it is probably best to stick with that time slot consistently to accommodate the natural rhythms of the body. For me, during the week, I am used to 4:30-7:00 PM but last year I got used to 6:00 AM, although I did get injured more often during that time. On the weekends, I prefer 8-11:00 AM.
These last couple of weeks, I have been getting my training in but much later than what is optimum for me. The upshot of that is my enthusiasm, motivation and energy is diffused. Mentally, I am not as focused either. I run the risk of injury on the sessions I lift heavy. I have to reset myself and get to the gym earlier and enjoy the more focused and quicker workouts. When I do train within my time range, the workouts are done at a quicker pace and I am out of the “box” much sooner than when I go later in the evening, like tonight.
This evening, going in later, I did 7 x 3 back squats and sure enough, I wasn’t very sharp. The other night was the same thing: late and lifting heavy deads. While I did get a PR, I had poor form and did risk injury, especially on the latter sets.
I did switch from the higher Olympic style squat to lower on the back the way powerlifters do it, per Mark Rippetoe.
7 x 3 at 135/185/225/225/245/225/225. 60-78% of 1RM.