I am not a morning person, and me being in the army really doesn't conduct to my love
of sleeping in. So, I deal with it and do what I have to do. Some days, I feel like I adapt.
Some days, however, kick my ass and all I want to do after work is take a nap. If I do that, it usually kills my workouts, besides, by the time I nap, wake up then workout, my eveining is shot.
I don't know if you'll get used to the schedule or not. After two years of this, my body is still in shock when that alarm goes off at 'zero dark thirty'.
I think the best thing to do is to drive on, and work through the tiredness. Even if you are beat after work, make it a habit to lift. Go light and easy if you have to, going light is better than not going at all.
Also, I warn you about caffiene. Sure, drinking a pot of coffee will get you going in the morning, but it will wear off and you'll crash by lunch. If you take caffiene for energy for the gym after work, it could keep you awake later than you intend, making the morning even harder.