At a startup / workplaces with that vibe where you don't actually have product influence what you want to do is track how the product progresses in relation to your thoughts on what you would do if you were able to influence the product. Consider literally every product decision and if you would have done that, or something else, and why / why not you think it would work. At some point you'll be able to see if those product features work out, or don't, and can compare that to your ideas on the subject. Hopefully whatever your thoughts are (whether constructive or destructive) towards the product decisions match what actually transpired more often than not, then you probably at least are able to have a finger on the pulse for what's good / bad. For me, a lot of it isn't always knowing what the right decision is, but knowing what the wrongs one are (going down the wrong path too often or too deep is really how bad products are made).
If you're at a startup / workplace where you are able to insert yourself / your input into the product pipeline, then do so and see what happens. If you actually have good / valuable ideas and are able to push them into fruition through whatever current product infrastructure that exists at your company then that should be a plus as well.
I personally believe there is no replacement for having done it before yourself. As an engineer, building products for people whether they are clients, consumers, other business, etc directly are what can give you the best product knowledge feedback. The most I learned as an engineer about building products people want was through personal interactions with consumers of a game I built, along with interacting with clients for applications being constructed and fielding feedback directly from their consumers.
Most of the above handles the "Product" side of Product Management, the rest is of course how well you work with people, but that probably goes without needing be said.