“I don’t have enough experience”
Here’s the truth about experience. There’s a level of competency clients and employers need you to be at before they want to be paying you company dollars. That part is true. If you can’t show them you’re capable of doing what they need, you’re out—it’s simple. If you can, they’re interested.
If you’re willing to pull in extra work to fill in the gap from where you are now to where you need to be, do it all and show them.
When it comes to creative work, you don’t need someone behind your back directing you what to do. Experience doesn’t have to come from holding related jobs, but you do have to put in more work than just the brief from the classroom.
Instead of “I don’t have enough experience for these UX roles on the market” try imitating the work that passes through the screening and the interviews. That way you can start to understand what you might need to do more of.