Looking up at the work of very good young researchers, I have found that very early, they know a lot of stuff. I wonder if they learned all of this by reading or if there is another way of learning because sometimes, it's just too much.
Is there another -more efficient- way of learning math instead of reading (with pen and paper) and filling gaps in proofs?
Solve problems. Solve a lot of problems. Try every problem that interests you, even if you can't complete a solution.
One good way do do this is to hang out here on MSE. Surf problems and try your hand. Read the linked citings.
Solving problems is different than completing proofs, although I would consider proof completion as a branch of problem solving.
I'm not the first person to suggest this; indeed, far better mathematicians than Yours Truly have recommended this method.
This sure as hell worked for me, and keeps on working.
I'd be interested in hearing back how this works out for you, should you choose to give it a go.
Best of Good Fortune (Luck) with it!