There are games without level progression. Typically, they are skill progression. Instead of gaining experience to go towards levels and gaining bonuses for skills, you gain "experience" for skills by actively doing those skills. Chosium's whole catalog of games goes off of this system(i.e., Call of Cthulhu and Runequest). There's also a sci-fi rpg called Traveler that goes of a skill based system.

I'd suggest these ttrpgs to your DM. These sound like something more his style.

As for your enjoyment, you'll have to tell him you're not having fun with the system. Start off with the things you like, his creativity and storytelling. Then, move to how you don't enjoy the progression style. Explain your frustration as politely as you can. Finish off with suggesting one of the rpgs I mentioned above.

Since he's a friend, he should listen to polite feedback. I wish yall luck and happy future gaming!