It's surprising then there's a great camaraderie amongst writers. It's a wonderful community with as much support as any given writer wants or needs. The reason is because every single writer knows how tough it is getting started and maintaining a career. Every writer will at some point experience the ups and downs of what it is to be a struggling or working writer. Every writer knows what you are going through because they have too. The key is determination and resilience.
First of all your writing has to be top notch. It won't do you any favours going off half-cocked and sending out work that isn't ready, or that hasn't been proofread. That, as a writer, should always be your first priority. It's always worth getting a professional reader or two to check your work and recommend changes.
When your work is the best it can be, it's time to send it out. Reseach the people you are sending it to. If they don't make the genre of screenplay you've written it's a certainty they won't be interested. If they don't accept unsolicited work, move on. Don't waste your time or their's. As for competitions, make the most of them. Enter as many as you can, not just the big ones, but the smaller ones too. Competitions can be a fantastic measure of how good your work actually is. The better you do, especially the more consistently you do this, the better the writer you are.
Network like crazy. Go to every event you can fit into your diary, even the ones you can't afford. You can always crowdfund your ticket or borrow money from your partner or parents. Put yourself out there and make a great name for yourself as someone who is polite, enthusiastic, hardworking and reliable. The more people you meet and connect with the greater your circle of influence. Be brave. It can be great fun if you let yourself enjoy it.
If you see an opportunity advertised, or a friend highlights one online, have a screenplay ready to enter. If you're thinking, "I won't bother with this one because I don't really stand a chance," think again. The more initiatives, jobs and competitions you enter or apply for the more your chances increase. If you limit your opportunities to just one or two a year, then don't be surprised if you don't get anywhere. You have to be in it to win it after all, so be willing to take the risk.
Last of all, don't let the competition get you down. Concentrate on what you're doing and forget about everyone else. Don't compare your career to other writers, you'll only end up being disappointed. If you get turned down for a job don't stress it, just look for more opportunities, at whatever level, and go for them.
Even when you're an established writer you'll be turned down for work, your awesome new idea will be rejected, probably multiple times and you will be fired from the odd job now and again for creative differences. It's the same at all levels of writing. And it'll never change.
As long as you learn not to let it bother you, you'll be okay. Work hard, hunt down those opportunities and make the most of them and apply for everything even if you think you won't succeed. Successful writers are successful because they put themselves and their work out there on a constant basis. They never take their foot off the accelerator. They get on with it and don't let other people's success or doubts get to them. They write and send stuff out, write and send stuff out, day after day after day after day after day after day. Be that writer.
Happy writing!