I had applied to internships on their website. I was contacted by a recruiter via phone. I had a brief conversation about my skills and interests in SpaceX. Then we had set up a time for a phone interview with the Test Engineering Manager for about a week away.
That interview went well and within a week, they had gotten back to me asking for references and completing a background check. I wasn't sure if I had gotten the position at this point, but from what I had researched, it was a pretty high likelihood. Once the background check cleared, they gave me an offer. Background check took about a week.