Girl here.
So today was the first time a guy asked me out and I agreed because I like him; and it's a first for me.
Thing is, we can't go out yet because he had an accident and his knee is in screws and will take around 5-6 months to heal.
But he said we'd most definitely hang out after that.
But I wish there is something I could do if we can't go out just yet.

So what do I do? :3

I'm a guy.
I'm assuming your idea of "hanging out" is like going on a date. If that's the case, I would take the time to just "be friends" and nurse him during his injuries. That way, you can at least learn more about him and take it slow. When he is better...hanging out should not be a problem anymore.
I know because I broke my femur my Junior year of high school...and didn't really date my girlfriend until my Senior year because I wanted to get better. However, she talked to me at times and at least grown an interest when I was able to walk properly again.