Each house of Congress is the judge of its own members' qualifications and elections returns, and together they are the judge of the qualifications of the Presi

Each house of Congress is the judge of its own members' qualifications and elections returns, and together they are the judge of the qualifications of the President and Vice President. In principle they could allow Musk to become President; in practice it would never happen. (It's also possible that the courts might step in and forbid some candidacy on qualification grounds, but I think that's unlikely.)