Theory: brute-force key search
Sure, it's possible. In fact, this is exactly what the Large Bitcoin Collider does - It has successfully located a few private keys, mostly from a puzzle transaction that seems to have been made to test its progress.

That said, it would still take you an unreasonably long amount of time - The Large Bitcoin Collider took 1 year and 3 months to search 8,000,000,000,000,000 keys (8000 trillion).

There are 2^256 possible keys. Even if you are able to search 1000 trillion keys per second, it would take you 2.7×10^44 × age of the universe to go through all the keys. It's simply not feasible.

As pointed out by G.Maxwell in the comments, the Large Bitcoin Collider should be not be interpreted as a viable, secure, or even reasonable approach to this problem. There have been concerns about its safety and accuract (reddit source).