My prior understanding of "upstart" is the second from the dictionary : "an arrogant or presumptuous person". Looking it up I found that it derives from the meaning you intend: someone who has recently risen from poverty to wealth. In any case, it is not common to describe them. While some may have that characteristic, I'd suggest something more neutral like "more and more people are becoming wealthy".
Nouveau riche (French: 'new rich' [nuvo ʁiʃ]) is a term, usually derogatory, to describe those whose wealth has been acquired within their own generation, rather than by familialinheritance. The equivalent English term is the new rich or new money (in contrast with "old money"/"vieux riche")
I agree with Packard that "nouveau riche" could be used to describe these people, but we tend not to use the phrase as a noun. That is, we wouldn't say "a nouveau riche has emerged," nor would we say "many nouveaux riche are emerging."