The path my mother followed (as a doctor for humans) was to approach an existing physician about joining that physician's practice. She joined, the patients got used to her, and she bought out the practice when the other doctor retired a couple years later. This was the first thing she did after leaving medical school, but obviously there were a couple years in there of being the junior physician in the practice, which gives some time to gain experience.

She gives me to understand that changes in the legal landscape have resulted in US doctors mostly abandoning the idea of having their own practice in favor of being hospital employees.

There are no experience requirements for being your own boss.