I am writing a novel that I have every intention of writing as part of a trilogy. My question is if a publisher will look at me? I have never been published and the book I have in mind has three parts that each deserve their own title. I mean "Part 1" is already almost 300 pages. Is the fact that I am un-published going to hurt my chances of seeing all 3 in print?
No. What will hurt your chances is if book one doesn't sell. And it might not sell if the reader doesn't get a complete story out of it.
So, in my understanding (and I am in a similar situation to you), the first book needs to be complete. Full stop. And good, and probably not 300 pages although if you are fantastic 300 is OK too.
The advice I have heard that sounds right is to make book 1 as awesome as you can, that might mean don't save 'the cool stuff' for book 2. Make book 1 complete. When you pitch your book, be certain (and say) that it 'stands alone with series potential.'
You will find agents and publishers that specifically want new voices and new stories, so your lack of a track record is OK. You don't have the advantage of being known, but you do have the advantage of being new.
Edit in response to comment:
I am not published, but my understanding is that the book needs to be crafted so that it seems satisfying. This might mean adjusting the problem at the front end. Note: You know your ultimate arc. But, you can adjust it so that book 1 identifies only a portion of the arc as the problem.
The ultimate goal in Star Wars was (is) for goodness to prevail - and they still haven't pulled it off, and it's annoying. But Episode IV set up a smaller problem: Destroy the Death Star. That's it. That's the problem to solve.
They did, so the movie worked as a standalone. Vader spun off into space, which did two things: Communicated "He's taken care of for this story" and also allowed a second story IF the first one made money.
Imagine you're the publisher. Your only goal is to sell a good book. If as a publisher, you can help grow an author, great, but you are doing it for your business not because you care about a stranger who has a story.
The publisher will print your book if they think it will sell. If it does sell, then they might print a second book.
My advice as someone in your situation (I have five trilogies in mind for my world) is to wrap up the story satisfactorily. Leave enough enticing bits but they should not be loose ends. (In my story, there is a mountain tribe alluded to but they are a minor plot point. They are not a loose end, and the plot does not rely on them, ... but everyone who reads my story does say, "I was curious about that tribe that popped up in the mountains once."
That tribe is a big part of book two. If book two never happens it is OK, but if book 1 is successful then I have momentum with the tribe (and some other items) for book 2.
Also, I killed my Vader-figure, who is called the villain throughout, but I did not kill the apprentice Vader (who was never very scary in book 1) nor the emperor (who is the true villain - but never called out as such in book 1, is barely mentioned if at all, but is the target for book 3.).