UX is a tough one, I'm still unsure what the magic bullet there is as I personally believe a lot of itself is generally handwaivy. It's one of those things that you just have some magical touch with (which approximately no one has so don't be foolish and believe that you're the one), or something you gain over time through trial and error.

It's probably hard to get into a UX role that doesn't involve UI as well. So one side of that is being able to actual design UI, and build out some random "product" ideas with the various current tools available which allow you to design UI + make prototypes that seem real (something like Sketch, there's tons of others). This can be helpful for getting some experience together on your own time which hopefully could get you a junior UI/UX somewhere.

The other side of things is being a UI driven developer and try to get in as some sort of frontend UI/UX engineer which deals more with making user experience better vs fleshing out the business logic / internals. These sorts of jobs tend to exist more at larger shops / enterprises than smaller ones.

The third side (yea, this one has three sides) is to just try and get a foot in the door as a junior PM and grow from there. I honestly don't believe this is the best route as I think all it does is breed "pointy haired managers".

I really believe you need some experience in a space before being able to be a good "* Manager" of any kind, whether that be project, product, engineering, or otherwise.