For me the ability to improvise music emerged slowly after doing a lot of playing other things by ear and embellishing songs either from lead sheets or coming u

For me the ability to improvise music emerged slowly after doing a lot of playing other things by ear and embellishing songs either from lead sheets or coming up with premeditated variations on pieces I already knew. But that's just how I did it. If improv is your goal then you could probably benefit from doing it in a semi structured format like 12 bar blues, where it can start very simple and you can build up complexity.