Of course there is! The answer is incredibly simple: Just write the best thing ever written. Wow. I've given this secret away for free. How foolish of me. Now everyone is going to write the greatest thing ever written, and Hollywood will never be the same.
And therein lies the problem. When you're not in a writers' room or on a show as an assistant, you're competing with everyone else who thinks they're "above" an assistant job, or thinks their MFA is experience enough, or just got here off a bus with a Modern Family/Alf crossover spec that the writer thinks will really "turn the industry on it's head." Your "greatest thing ever written" goes on the stack with all these other people's "greatest thing ever written," whether that stack is on an agent's desk, a fellowship submission, or in the e-mail inbox of a patient writer willing to help out their cousin's neighbor. You've done nothing to differentiate yourself from the masses this way, and even if your script really is the greatest thing ever written, when you're not working in a writers' office, you have to ask yourself: "Who will read this?" Once you have that answer, follow it quickly with another question: "What will their reading it get me?" If you have an in with a showrunner, and they read your script and say, "It was good but not right for our show," what do you do next? You have nothing other than a pat on the back. More than likely, they'll give you notes, which you can take or leave, and nothing else happens after that.
This is the main plus to working in a writers' office -- you have a bevy of people at your disposal who will most likely try to help you. You have a group to read your first draft for notes, a second group to read your second draft for clarity, and a third group who can pass that script along to their agents, or the studio, or anyone else who can try to help you get a writing job.
So if you're not inside that writers' office -- how do you break in? Well luckily for you, there are over 400 scripted TV shows being made, and all of them need people to help. People to help assist their producers. People to help in post-production. People to help on set, in the production office, or even in the agencies and management companies that represent the people working on the shows. These non-writers' room jobs will help you do something as important as writing the best thing ever-- pay your dues.
Someone who has paid their dues by putting the time in and doing the best job they can on the job they have will almost always get the opportunity to move into a job they want. At least, it will put them ahead of the people who look down at jobs that "don't fit their MFA" or those who "just need their producer cousin to take their calls." People who have made it to the writers' room respect people who have paid their dues more than those born on third base with a three-picture deal on the horizon, I assure you. Hard work, determination, and a great attitude may sound like cliches, but they're also the common link of the people who succeed in the entertainment industry, no matter where they start in it. Sure, you may not start in the writers' room, but the life experience you amass on your way there will only give you more to write about when you get your seat at the writers' room table.
Of course, you may just write the best thing ever, find the right person to read it, and skip all these steps. If that happens, find me and let me know, so I can put you on my list of people who worked their way around the system. Just know that as of right now, that list is blank.