I will throw up a program that is completely arbitrary, with nothing beyond theory and personal opinion. With that said, I think it's a solid primer for fitness for combat sports.
I would join the bjj/boxing gym asap. You'll progress quickly and will be glad you gained the knowledge without wasting time.
Still, you asked for it, and you're getting it.
Assuming no access to bags or partners
--Rope work--While wearing mouthpiece (you mention MMA, so you need to get used to keeping your mouth shut and exercising)
Pace of 100+ Rotations a minute for 3 minutes
Shadowbox for 3 minutes, with movement, intensity
20 burpees, jump sprawls, or squat thrusts
20 pushups
20 leg raises
Repeat x2
If you can accomplish this, you should join a gym asap. If you can do it once, you should join asap. If you can't make it through ropework, then yeah, you'll gas before most gyms' easy warmup is over.
The workout isn't anything extreme, and it's not what I'd do to get in competition shape (not that far off either). If the average person asked me what they should do for a couple weeks before they could join a gym, this would be pretty close.
Still, this is an easy way to justify quitting before you start.