Clearly the term "America" either disambiguates to a continent or a country, and most assume the country.
"Europe," on the other hand, really is a continent, so the term has a completely different meaning than the EU, although it would be reasonable for the two to be synonymous eventually, they clearly are not currently.
Anyway, it seems reasonable to use the term America as shorthand, instead of U.S.A., as it's pretty obvious what you mean.
https://en.wikipedia.org/wiki/Americas
"The Americas, also collectively called America"... In many languages America is the continent.
The wikipedia link to America, redirects to the United States of America: https://en.wikipedia.org/wiki/America
And in the description of the United States of America: The United States of America (USA), commonly referred to as the United States (U.S.) or America
https://en.wikipedia.org/wiki/United_States
Also see: https://en.wikipedia.org/wiki/America_(disambiguation)
"America is a short-form name for the United States of America."