This is correct. In the U.S. you would almost ALWAYS write: May 4, 2021.
You would speak out loud :”May 4th, 2021” even if it was written the other way.
For example you would SAY: “Can i make an appointment for May 4th 2021?” and the Secretary would write it as: May 4, 2021.
(And if you are a Star Wars fan you would say, “May the 4th be with you!”)