Latino peoples are a product of the inevitable merger of African, European and Native American people. You can see it in their religion, culture, DNA and cuisine....so much so that they are one of the ethically unique yet diverse groups in the world ..but I wouldn't say the built this country. More like this country/Americas built them.
Historically, like African Americans, Latinos are far better at culturally adapting to societal changes while still maintaining their cultures, compared to other groups. Their greatest advantage are their numbers. Because of this, Latinos have the potential to shape America far more than any of group in this nation. Especially since ws have used them as a buffer class/group against Blacks, for centuries. Cacs are not using Latinos to fix their own pop numbers, to stop the falling birthrate bleeding.
A more accurate statement would be, "Latinos are building this country". And that's true in more ways then one.