I've posted a few times on here in the past weeks and through those posts I've received a lot of good advice, I've started developing a small game as more of a showcase for what I can do but plan to continue working on it until either it's done or I'm done with it. I know this is probably putting the cart before the horse and the likelihood that I take a game to this point is small but out of curiosity if I got serious about developing it what does pitching a game like this to a larger company entail? What would be some things I could do to make it more appealing, and at what stage would you suggest attempting that, fully finished?

Wrong forum. You're asking a Business question, not a Career question. The Career Development forum is for questions about getting a job, moving up in a job, work-life balance, etc.

Moving this to the Business/Law forum, where this question was asked and answered in the last day or two. Scroll through the Business/Law forum, check the thread titles. And read https://sloperama.com/advice/lesson21.html​

This one was posted just yesterday: https://www.gamedev.net/forums/topic/714079-best-way-to-sell-a-game-idea/​

This one was posted in Careers just yesterday, and may be relevant: https://www.gamedev.net/forums/topic/714081-how-to-make-an-idea-seem-unique/​

Let me note here that “big companies” (depending on what's meant by that) are not the only ones available these days, and that indie publishers do, I believe, take pitches.

For more information, I'd suggest reading the relevant entries in the following series of articles:

https://ltpf.ramiismail.com/archive/