A guy that was instrumental in making American (as in the US) classical music sound American and not European was the Czech composer Dvorak.
By the end of the 19th century American composers were trying too hard to sound German (not surprisingly, given the quality of the composers there). To change this trend Mrs. Jeannette Meyers Thurber (the funder of the National Conservatory at New York) appointed Dvorak as the Director of the conservatory (so she should be credited with that idea). It may sound sort of strange that Mrs. Thurber called a Czech composer to start making true American music, but one characteristic of the 19th century was the rise of nationalism. Many European composers (like Dvorak) were fascinated with folk music, and more than willing to mix this type of music with their compositions.
Now, the sources that Dvorak used to learn and incorporate American folk music into his compositions were not that solid: he hired one African American to sing spirituals to him (though this guy was very good), and learned about Native American music by going to Buffalo Bill’s “Wild West” show. On his behalf it has to be said that it was not that easy to get first hand access to that type of music at the turn of the 19th century in New York. Some of these influences were allegedly used for his New World Symphony, which was a big hit at the premiere. Well, it was a big hit at New York ,some people at Boston considered it to be a lesser composition since Dvorak was trying to incorporate music from African Americans and Native Americans (how dared he!). It is disturbing how racism can be more powerful than taste or reason; that symphony was (is) superb, and I think those music critics knew it but could not even acknowledge it.
One more thing, I find it almost funny how the whole idea was to produce something uniquely American and not just copy the Germans, but the start of Dvorak’s scherzo is an almost exact copy of the first measures of Beethoven’s scherzo. I know it is a wink or homage, but it does give the idea that some people are just unavoidable (and rightly so). Here are both beginnings (it is only the first few bars):
And here is the complete Symphony, if anybody cares