I don't know what year would have been the 'turning point'. But I do know that by 1750, the British North American Colonies counted 1.5 million people, exclusive of Native Americans, and African slaves.

@misterinvisible, @corroboree, @BD66, @t1nick, @KKGator Thanks for all of your responses. I am well aware that this is not supposed to be white land. I have been aware of the genocide and forced evacuation that cleared it since I was a child. It is strange to me how recently these things happened. The trail of tears happened in the 1830s. The mass reeducation of Native American children happened throughout the early 1900s. Its discusting and chilling especially once you take slavery into account. The sheer size and organization of the operation is hard to grasp. I have heard that there were more slaves than white people in places in the south. It just got me thi king if we ever really were a majority anyway and for haow long.
I did a very brief google search on my question. From what I have read here it looks like there is no ready and obvious answer to be found. Thanks so much for your input I may have to look further into it.

Another good title is "Custer died for your sins'

For a better handle on the "little people" who's backs this great country was built upon I would strongly urge you to at least skim through Howard Zinn's "The Peoples History of The United States of America" highly informative.

Off the cuff and prior to any serious research.. I'd speculate sometime after columbus' landing in the Bahamas (whereupon he spoke of the natives in his journal and I am paraphrasing for context here; "these people are so generous and giving and a beauty to behold, I only wish I had some guns and swords whereby I could subjugate them".. sometime after that until somewhere around the time that Custer with his United States Army Troup lost the battle of Bighorn to the Lakota Sioux which at the time was Monroe Doctrine to the United States.

Whites probably started to outnumber Native Americans in the 1760's and 1770's. There were 3,929,214 people in the USA (mostly white) in 1790. Nobody knows how many Native Americans were here before Columbus arrived, but their population was falling rapidly due to European diseases in the 1760's and 1770's so that's likely when the crossover occurred and whites became the majority.

It is known.

Between 1500 and mid-1800's westward expansion by Europeans marginalized Native tribes into smaller and smaller areas of land using the excuse of Manifest Destiny. The largest human genocide in human history occurred during this period across both the Americas.

Numerous atrocities against Native Americans span the hundreds of years from the first arrival of European explorers to the modern era under a wide range of circumstances. Today there are over 500 Native American tribes in the United States, each with a distinct culture, way of life and history. Even today, Native Americans face large challenges to cope with the disadvantages history has left them and ongoing cases of discrimination.

10 million+ Estimated number of Native Americans living in land that is now the United States when European explorers first arrived in the 15th century.

Less than 300,000 Estimated number of Native Americans living in the United States around 1900.

5.2 million identified as American Indian or Alaska Native in the 2010 census

Disease
The most significant reason for Natives decline was disease – an invisible killer that wiped out an estimated 90% of the population. Unlike the Europeans and Asians, whose lifestyle had a long history of sharing close quarters with domesticated animals, Native Americans were not immune to pathogens spread by domesticated cows, pigs, sheep, goats, and horses. As a result, millions were killed by measles, influenza, whooping cough, diphtheria, typhus, bubonic plague, cholera, scarlet fever and syphilis.

[endgenocide.org]
Atrocities Against Native Americans

For example, in the case of the colonization of the Americas, where 90% of the indigenous people of the Americas were wiped out in 500 years of European colonization, it can be debatable whether genocide occurs when disease is considered the main cause of population decline since the introduction of disease was mostly unintentional.

[en.m.wikipedia.org]
Genocide of indigenous peoples

The population figure of indigenous peoples of the Americas before the 1492 voyage of Christopher Columbus has proven difficult to establish. Scholars rely on archaeological data and written records from European settlers. Most scholars writing at the end of the 19th century estimated that the pre-Columbian population was as low as 10 million; by the end of the 20th century most scholars gravitated to a middle estimate of around 50 million, with some historians arguing for an estimate of 100 million or more.[1] Contact with the Europeans led to the European colonization of the Americas, in which millions of immigrants from Europe eventually settled in the Americas.

[en.m.wikipedia.org]
Population history of indigenous peoples of the Americas

If I'm going to guess, I'd say roughly mid-19th century.

I'm adding a link to Quora that may offer info on this subject. If the link works you should be able to click around onto other related subjects there. I hope this helps.

Read "Bury My Heart at Wounded Knee."

Not the movie.

The movie is a joke.

It probably happened when the white man slaughtered so many native Americans.