You need practice, sure. And there's never an assurance that you'd be able to solve difficult problems elegantly and with in a short time, or any difficult problem and always in short time.

T SAIDEEP

I would recommend the books by G.Polya, especially How to Solve It? and that of J. Mason, Thinking Mathematically. Check

https://www.math.utah.edu/~alfeld/math/polya.html

To get good at doing proofs, you need to learn some basic logical tools, and then you need to practice, practice, practice. And even this is no guarantee that you will always quickly come up with an elegant solution. Proofs require knowledge PLUS creativity PLUS logic PLUS time and hard work. Fortunately, they can also be challenging in a fun way, once you start getting the hang of them. Try looking at them like games or puzzles to conquer, and maybe they won't seem so bad!