The more I exercise, the deeper and more quickly I sleep.
And timing doesn't matter.
When I lived on my own, I'd often cycle until 9 or 10 pm, then do a bit of yoga and/or weightlifting, catch up on some housework, then relax for about an hour, and I'd be into a deep sleep about 2 seconds after my head hit the pillow.
Now I don't exercise quite that late, but even so, one sure way to get a great night's sleep is to go for a decent bicycle ride or run at some point during the day.
I've even fallen asleep before my head hit the pillow if I've put in a large amount of exercise. I know there have been times when I remember sitting on the edge of the bed ... and 13 hours later, I wake up lying in bed, covered in my blankets. But I don't actually remember lying down.
And if I don't exercise much at all for a couple days, I'll have a restless night.
I second the suggestion about going for a sleep study ... at least do some reading about circadian rhythm