It does depend on your gymnastics coach, and also what basics / strength&flexibility you already have. Lots of clubs have gymnastics coaches teaching level 1 -3 that just teach those skills, and aren't qualified to teach the harder skills, but some do have the experienced coaches from the beginning, and if they think you are ready, you could learn something like the back flip or front flip or back handspring on your first day of gymnastics practice!
The levels/skills kind of go like this:
-forward roll/backward rolls, handstands, back extension roll (backwards roll to handstand, with bent arms, then with straight arms), handstand forward rolls
-back walkover, front walkover (depending on the gym and the club you might be doing back/front bends or tic-tocs before this, or while learning this), back handspring, front handspring
-back flip, front flip
...then you build on those, put skills in combination...
on bars:
-pull-over, back hip circle, underswing dismount, front hip circle, back hip circle, shoot through circle (one leg over the bar, with undergrip you go around the bar), squat on, swings on the high bar, flyaway (tuck dismount from the high bar), layout flyaway, cast flyaway, giants on straps, ....
on vault:
-you might do squat on vaults and squat through vaults first
-the first part of the handspring vault, jump from the spring board, push with your hands, and land on your back on a soft big mat
-then the handspring mat
-then the tsuks, half on vault - kind of a roundoff off the vault table
beam:
-dance elements, basic turns, walks, then handstand, cartwheel, handstand half turn dismount, backwalkover on beam, front flip off beam, back handspring on beam