I began programming on a Tandy TRS-80, but today I primarily work in Angular, Node and TypeScript.
I have no formal training.
So yes, with the right experience for the role, you don't need a degree.
When I'm interviewing candidates, the last thing I care about is their degree.
I want to know what their passion is, how they approach solving problems, etc.
Regardless of whether you're self-taught, being able to demonstrate your work on Github or a personal site is an absolute must.
Experience takes time to acquire. Be patient. Work on and learn what you want to be doing in your spare time. That will pay off faster than anything.
One thing that may help is to put up repos of stuff you've worked on, on GitHub.
Contribute to open source projects that align with things you're interested in.
The key to getting work at more and more places, it's not whether or not you have a degree... it's being able to demonstrate that you know what you're doing.