My path was a little different, as I am neither a developer nor someone with an MBA - I worked on some personal projects early on (startups, tech focused non-profits) where I demonstrated basic PM/getting the right things done skills, and I combined that with some early experience I had as a program manager at Microsoft and as an undergrad intern within PM groups at other companies.

In terms of how to start, the 3 ways I can think of are:

1) Work as an engineer for some time, try to pick up roles such as being the scrum master, managing sprints etc. (or whatever equivalent your team is doing), then get an MBA - many companies will hire you for PM right out of MBA school with no prior experience

2) The program manager role at Microsoft is one of the few places where you can start in a role that is essentially junior product (they hire undergrads right out of school). If you can find other companies that have roles like this, that's one way to get into the PM role. Another one is Expedia I think, an MS spin-off.

3) Another way would be to go work at a startup where you can add PM input and grow into the role. This is what I would pick if I were to start over again.

Generally speaking I think companies are open-minded when hiring for the PM role - you don't have to fit an exact formula. In my experience people look for evidence of the following in your background:

1) Being able to think big and be truly creative

2) Being able to ship products (preferably you've actually shipped something already)

3) Being comfortable working with data (though my 2c is that we're over-doing this)

4) Having good decision-making frameworks for why, what and when the org should be building things

5) Being able to dive into the weeds of any domain without hesitation.

My team at Amazon is hiring PMs by the way. If you're interested in talking, feel free to send me a note.