Impossible. America, like all settler colonies, is predicated primarily on the promise of wealth and political supremacy for the settler class, which has expanded over time to be simply defined by whiteness rather than just WASPness. The entire social contract that underpinned slavery, Indian eradication and the rest was white supremacy; immigration was open so long as the basic tenets of that contract weren't seen as threatened. We can see this with what restrictions were placed and when; Asians were banned early, when they "threatened" to undermine white supremacy in California both in labor and in culture. Southern Europeans and Jews were restricted later, so as to prevent what the powers-that-were saw as a tide of subaltern people ready to undermine the white-supremacist social contract. Black people have been held under the jackboot of law and society for the entirety of our history, treated worse than most immigrants, a conquered people inside their own country. And their labor migration was itself restricted -- both in what neighborhoods they could settle and whether or not they could leave (Jim Crow was firstly a way for Southron elites to prevent the drain of the black labor that sustained their postwar -- and prewar -- society.)
Above all else, that singular idea -- the social, political and economic supremacy of white-coded settlers -- rules not just America but the entire New World, Australia, New Zealand and Israel, just as it ruled Algeria, Rhodesia and South Africa pre-Mandela. It is the sociological basis for our society, the very reason this country exists. To open immigration to all peoples from the start would be a negation of the basic premise of America's existence, and would spark an immediate, furious backlash. Imagine Know-Nothings on crack -- this was a country that was only a few decades removed from seeing fucking SWEDES as swarthy (in the words of Ben Franklin).
A non-racist Amerikkka is a contradiction in terms.