The population of Great Britain and France has increased about 1 1/2 times in the last 150 years; that of the United States has increased about 10 times. Some of it was no doubt due to higher fertility of Americans compared to the French and the Britons, especially before the frontier closed, and farming families were large. Most of it, no doubt, was due to immigration. I cannot find any numbers on the Internet, but it seems intuitively obvious to me that the ancestors of most Americans alive 150 years ago were not resident in the United States. Mexican Americans are about 10% of the U.S. population; there were very few of them in 1863. Italian Americans are about 5%; same here. American Jews are about 2%; same here. Polish Americans are about 3%; same here. Immigration from Germany in the 2nd half of the 19th century was huge. 12 million people came through Ellis Island alone, and they had children, and their children had children. Therefore, if "stole their land" you mean "won the Mexican-American War", then it weren't ancestors of most modern-day Americans; it was other people in the country to which the ancestors of most modern-day Americans later immigrated.