Musk isn't running for Trump's job, yet. Right now, he is unable to be President, our Constitution doesn't allow him to be. But Trump &Co do not seem to be bound by pesky things like the Constitution and laws, so anything can happen.
This is all a stunt to make himself feel better IMO. A person can't just create a political party and start winning elections. There are rules and steps that must be followed and it is a long process.
He would be better off funding primaries against sitting members of Congress for 2026. I predict that his next step will be to do just that and The American Party idea will fall to the wayside.
Unless Tesla continues on his downward spiral and he runs out of borrowed money to live off of.