I have had an idea for a video game designed around narrative. I don't have any experience in the field in the past so teams won't just let me onboard. Because of this, I would like to write the script first and then show it to a team and find someone who would take the script and turn it into a game (I dont want any payment for it).

I have been developing an idea writing notes for the last 3 months and I am ready to start writing the actual script for the game. If I write the script, then where can I show it to see if a team would like to take the script off me for a game?

Thanks in advance

I would like to write the script first and then show it to a team and find someone
who would take the script and turn it into a game (I dont want any payment for it).

Read these:
http://www.sloperama.com/advice/idea.htm
http://www.sloperama.com/advice/lesson11.htm
Those refer to the mainstream industry, not to indies. In regards to indies, I'll
just say that most of them already have ideas they want to work on. They might
consider your script as a portfolio piece, but then they'd want you to write what
they want. This is not to discourage you. You SHOULD write the script. Then,
after that one's finished, write another. And keep networking!

Truth hath been spoken here.

Everyone making video games is doing so because they have a video game idea they wanted to make. If your idea isn't strong enough to get you to learn to make video games, then it won't be strong enough to get anyone else to either.

I usually don't support trolls, but I would love to see a thread where someone claims to have a top notch video game team and they're just looking for someone to give them ideas. Of course, iirc, I think someone's used that as a marketing gimmick and ended up just making the game they wanted to make in the end. I can't remember the name of the project though...

I would say that you should look for jobs with studios, both indie and main stream. Send them samples but DO NOT send them your original idea. Instead, get the job, work for them for a couple of years, and then present your idea to the team. That's how most people do it in both games and TV.