Good product work isn't about ideas or intuition. It should be primarily a research job. You learn about users, work with the team to solve their problems, and then close the loop by testing it with users.

Lots of companies hire people for product work who have no idea what they're doing and no experience doing it. Those people often seem to come from marketing at other firms.

I know I've just outlined a catch-22 for you, but that's unfortunately how some roles work.

My recommendation is to get some quantitative digital marketing experience or approach from the engineering side or offer to do product work for a FOSS product. An example might be something like KeepassXC.