But how many of the characters were explicitly from America?
IIRC, only Tyler was given a home town.
You're right that - similar to LaForge or Seven of Nine - some of the DIS cast could always be retconned into being not American. However, they didn't even really try.
Accents: Not only did they not attempt to have the American/Canadian actors who played human characters portray characters with an accent, Isaacs and Latif didn't use their natural British accents despite every prior Trek having had at least one character with a British accent. Isaacs choice was apparently his own, because he didn't want to be compared to Patrick Stewart, but we don't know why Ash Tyler was made canonically from Seattle. It's also important to note here that the show did make the actors playing Klingon roles speak in an accent (except maybe Kol - I don't remember him having an accent once the UT started working), so it's not like that sort of voice work was beyond the case. This is the first Trek since TOS to have a large proportion of the cast speak with something different than their natural accent (Troi's weird dropped accent in early TNG aside), so it's weird that it was done in such a way to make things more culturally uniform. Georgiou is obviously the exception, and very much appreciated.
Surnames: Most human characters in the series have very boring Anglo last names. Burnham, Tyler, Tilly, Culber, Cornwell, Landry, etc. Obviously there are exceptions - Georgiou, Lorca, and Stamets, plus extras like Detmer and Owosekun. However, overall the last names of the cast seem far WASPier even than what I was used to growing up in Connecticut, let alone what you would find on a ship which purportedly has a global crew. To me this seems the oddest oversight, because you wouldn't need to change the characters at all to improve representation.
Other: Lorca is almost certainly at least partially American by ancestry, since he said his family ran a business that produced fortune cookies, which are an American invention.
But yes, there is no reason not to believe that Burnham's family was from Jamaica, Stamets is German, Tilly is Australian, etc. Still, everything which has been presented onscreen seems meant to suggest that the cast as a whole (except in cases where it is explicit, like Georgiou) is of North American background.