To get an “in”, you must network, which should include attending screenwriting seminars, workshops, classes, etc. You should also study movies and screenplays on an on-going basis to pick up on timing, rhythm, tone, mood, and read everything about screenwriting and networking you can get your hands on, etc.
The fine point of succeeding as a screenwriter is to utilize perseverance. It pays off. So, regardless of what stands up in front of you, you must utilize your passion for your work to overcome every obstacle, no matter how difficult it might be.
So, get out there and get after it!