If I were you (which I'm not...
), and coming from US to Europe with jetlag, I would simply get a hotel room and have a rest day in central Madrid (Atosha is just a 15 mins easy walk from Plaza Mayor).
This way, you will have no rush getting into central Madrid to your hotel for check-in.
Then walk to Atosha and buy a morning ticket for next day to Sevilla, then relax in/sight-see Madrid, have some tapas and a glass or two of red Rioja, get a good night's sleep, and then get on with the nice train ride to Sevilla the next morning.
But of course, if you have time constraints (which I don't have, as a retired), then it may not suit you. But doing all in one day will be a bit stressful/tiresome, and all depends on no delays/unforeseen events on your journey.
Anyway: Buen Camino! The VdlP is a great Camino.