TLDR: they have a strategy and they practice a LOT.
There are many different strategies for solving a Rubik’s cube, but the one most speed solvers use is called CFOP which stands for:
Cross – solve 4 edge pieces in a cross around a center
First 2 Layers – fill in 8 pieces around that cross
Orient the last layer – flip the remaining 8 pieces the way they need to go
Permute the last layer – move the remaining 8 pieces to where they need to go
The final 2 steps are fully algorithm based as others have mentioned. Lots of practice goes into memorizing sequences of moves and recognizing them.
The first 2 steps are what separates a good cuber from an amazing cuber. The best in the world are able to use the 15 seconds of inspection time to plan out these steps in their mind, which is about as difficult as you’d imagine.
I recommend videos by J Perm if you’re interested in a step by step breakdown of specific world record solves: https://youtu.be/B9MKizs9PUw
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