I ran recruiting at SpaceX for almost 6 years; everything about how they recruit is part of the footprint myself and my team created - so hopefully you'll find this input helpful, though it will only magnify the challenge that lies before you.
SpaceX aggressively pursues top collegiate talent; but because the hiring bar (mandate per Elon) is top 1% of the human population - we focus on top ranked engineering programs because their strict acceptance requirements are a good prefilter and remove 90% of the bell curve, thereby automatically bringing us to about top 10% of the college population; making our haystack much smaller and thus easier to find the proverbial needles.
Once within the top program populations we again filter aggressively based on:
1. Hands-on hardware/software development experience - i.e. What problems have you actually encountered and solved?
2. Experience with engineering competitions, and placement in top positions/brackets at those competitions
3. GPA/ SAT - other hard scores
The reality is that SpaceX makes some of the most magnificent machines on the planet (and beyond - yes, pun intended :). So the world's best engineers want to work there. That paired with what I've already stated means there is both an ability and a necessity to only hire people after they have in some way demonstrated themselves to be truly exceptional.
[I am not saying, NB, that SpaceX's criteria are good/correct/ideal (as a matter of fact, I think focusing on 'top engineering programs' may be the least good of their criteria, but maybe I'm wrong.) But I think that they're relatively clear and more importantly, well-publicized. (now anyway.) That's worth something.]