How do you upload it to github?
I've never done it this way, but I think you can literally create a repository/project and just click the Add file dropdown, then upload files. That would at least accomplish the basic Jam requirements of having your code there.
You can also set up source control, though, which can get a little annoying. I used Unity Collaborate, so that prevents it being set up within Unity. Me, personally, I just created my project in Unity, and as I edit scripts, it automatically creates the Visual Studio project if you're using Visual Studio, for example...
If you install Git, Visual Studio Community or whatever, you can go to Team Explorer in Visual Studio, add the project to source control, then there are Git tools built in, and you can publish your code right from Visual Studio as long as you have a Git account.
If you're not using Unity, you can just add the files themselves to a project in Visual Studio. Visual Studio Code would actually work nicely for doing that. You can install Git tools to make that easy in VS Code's "Extensions."
You tried what, exactly?
There's also Git Large File storage. I was doing a little reading and installed that as well before I did my commits, so maybe that's all you need to do, but I'm not sure. I don't know why there's a separate thing to install or if it even matters, but I read about that here: How to Git with Unity (thoughtbot.com)
Don't worry about the setting up of version control through Unity if you don't want to, you can just commit the way I mentioned below, I believe.