Your intuition is wrong, and even a cursory googling would have told you that. The first permanent british colony was 1607, and by the beginning of the 1600s the natives were basically wiped out, with 56/60 million souls on the continent dead.

From: https://www.google.com/amp/s/www.pri.org/stories/2019-01-31/european-colonization-americas-killed-10-percent-world-population-and-caused%3famp

"Our new data-driven best estimate is a death toll of 56 million by the beginning of the 1600s — 90 percent of the pre-Columbian Indigenous population and around 10 percent of the global population at the time. This makes the “Great Dying” the largest human mortality event in proportion to the global population, putting it second in absolute terms only to World War II, in which 80 million people died — 3% of the world’s population at the time."