The round that most distinguishes a SpaceX onsite is the past-project presentation. Candidates commonly report submitting about five project topics ahead of time, of which SpaceX selects one and asks you to present it for roughly 10 to 20 minutes to a panel of five to ten engineers, followed by questions.
The panel is not grading polish. It is testing whether you can defend every design decision when challenged, explain your work clearly to engineers from adjacent disciplines, show a bias toward the simplest solution that works, and stay composed under pushback. This is the loop making the hardest-problem question concrete: it wants to see the decisions you personally made.
The common ways to fail are instructive. Presenting a group project where you cannot isolate your own contribution, waving past the math, getting defensive when questioned, or glossing over what went wrong all read as weak signal. SpaceX VP of HR Brian Bjelde has said resumes should include your failures and how you overcame them, and the presentation rewards the same honesty.
Prepare a project you owned end to end, rehearse defending each decision and the numbers behind it, and be ready to say what you would do differently. The resume sets this up: the projects you can present are the ones you should feature.