You can’t technically do both at once. But you can make it appear that way. That’s the trick
Idk what you mean by “I’m out of shape.” You’re fat? Slow? Weak? That’s a broad statement.
I’m going to assume excess body fat. Start off building muscle. Muscle creates metabolism. The more muscle, the more calories you’ll burn in your sleep. So at least add 10lbs of lean muscle mass.
As far fasted training. Want to be small and weak? I used to train at 5am. Not my cup of tea, because I have to eat before I lift. But if I eat to soon, I’ll throw up while I train. Because I train intense. So I’d get up at 3am. Slowly, lol. Cook food, shower, let food digest. Train at 5.
You don’t have to get up at 3. But I suggest oatmeal with a couple eggs or steak. Whole food over liquid and liquid will make you feel hungrier as you lift. But whichever works for you. Just eat. You can’t grow if you don’t eat.
How much you weigh? Have a gut? Big gut? Little gut? No gut?
Also, what I like to do, is wake up, bust out 50-100 air squats and 50-100 jumping jacks. Empty stomach. Then eat, then go to the gym. Doing that workout will make you more insulin sensitive. It’ll wake up your brain and central nervous system. It’ll get your blood flowing and make your training session better