I have, as usual, an unpopular opinion. I think a completely unknown screenwriter with no connections or money has no chance. Most of my reasoning has already been written above.
I think in todays market you have to produce something directly for an audience, and gain traction that way. Let's look at Johnny Knoxville. He kept having his idiot friends kick him in the balls until he was rich, and now he has starred in a half dozen films. I don't respect him, but I do understand what happened. He bypassed the system completely, until he had proven his brand as a financial winner, and only then did anyone take notice of him.
I don't know if it's possible to write a breakthrough script in this era. I think it would be a far easier path to gain wealth, and then simply tilt the pinball table. Do you think Ariana Grande auditioned to become a singer? She was pushed onto the set at Disney in a stroller by multimillionaire parents, and the singing lessons came after. The film "White Chicks" got greenlit, and 80 million in total budgeting. Do you think someone read through 3000 scripts and picked it out as the best? Some executive got drunk and watched an episode of Mad TV where Damon Wayans poured a soda over his head, and then the studio guys pulled a lever on their desk that dumped 10,000 unopened script submissions into an incinerator room and made White Chicks. They will ignore 1000 of us to make room for Sandler to make a movie about "How a guy wants to play harmonica but no one likes it until they do and he becomes famous" the cruel irony being that they sell us a movie about how the little guy has a chance, while simultaneously engineering a system where he/she doesn't.
Sorry to sound negative, but all my experience to date has been watching rich people fail upwards, and poor people succeed downwards. Make some money, and level up that luck stat first. J Lo didn't take acting classes until she got good enough to make Gigli. Someone here said the system isn't rigged, and it's not, it's super rigged, like there is no chance for anyone who isn't rich, beautiful, or connected. Your best chance is to get rich, and rig it yourself, since that is far easier than playing someone else's caste game. Setting up a fire extinguisher store in Phoenix AZ is going to take a lot less time than lobbing your scripts over their wall of nepotism. Greenlight yourself, you could be waiting a long time for them to do it for you.