There are a gazillion ways to try to break into a career in screenwriting, but the least effective one is probably writing a script and hoping someone will pay you money for it.
A more effective route is making the movie and either submitting the finished product to competitions and festivals, or trying to get it on a streaming service so it's out there for folks to see. Or both!
Here are two options for making your movie:
Get a camera and shoot it yourself
Find a production company that will shoot it for you.
The first option involves a camera (or iPhone), some money to buy meals for your cast and crew (oh, and a cast and crew.) You can shoot your own movie for hundreds of thousands of dollars, or a few thousand dollars (or less!) See this in-depth article about how these two brothers did it.
The second option (finding a production company that will shoot it for you) involves getting other people interested in it. This can be friends who know how to shoot stuff, or you can submit to production companies. IMDb-Pro can be a useful resource for finding a company. Go small! Find a small production company that's looking for something to shoot.
But one caveat: regardless which option you choose, you'll probably want your movie to be relatively inexpensive to make (save your World War II/zombie invasion/Waterworld/trip to Mars epic for when you're rich and famous.)