We heard from some people who had returned from the US that free tests are available in the US. Most important, they are valid for Japan as long as the right documents are stamped. My son is in NYC and due to come back next week via ICN. He knows Japanese who have done this, supposedly the test is just 30 minutes. I guess it is the/an antigen test? It's hard for me to verify anything though.

Searching NYC in English I just see commercial testing for $200 or free NYC testing that takes 3-4 days.

EDIT: The Japan Immigration acceptable ECLEIA or CLEIA tests seem to be terms that only get hits in Japanese. The form warns ICA is not acceptable.