How many people today have ancestors who moved from Europe to the United States during 1900-14?
About 11 million people migrated between Europe and the United States during 1900 to 1914. Their movements can be traced in passenger lists prepared and recorded by shipping companies, and collected at immigration entry stations, such as Ellis Island (through which about fourth-fifths arrived). Because nearly all of them were born in Europe, and accurate passenger traffic figures show 10.8 million moving west to the USA, and 3.1 million moving east from the USA back to Europe during these years, it can be established that a net of about 7.7 million of these migrants ended up staying in the USA.
Practically none of those 7.7 million are still alive today, but a few of their children are, as are most of their grandchildren, great-grandchildren, and great-great-grandchildren. Each generation that can trace ancestry to a 1900-14 immigrant is larger than the one before it, and the rate of growth over time is surely higher than that of the overall U.S. population. (The high growth rate is largely a result of the sizable minority of such 1900-14 immigrants and immigrant descendants having children with people who were NOT 1900-14 immigrants or descendants. Note that, if an average U.S. couple had, say, three children, that would amount to 1.5 children per parent. But if one only parent was an immigrant or immigrant descendant, then there would be 3 children per immigrant or immigrant descendant. In contrast, if BOTH parents were immigrants/descendants, then it would be only 1.5 per immigrant/descendant parent). Thus, because of intermarriage with people not related to 1900-14 immigrants, the number of U.S. citizens with early 20th century immigrants as ancestors has grown, over the past century, as a fraction of the total U.S. population (even assuming (roughly) the same net reproduction rate for all U.S. couples regardless of ancestry).
The 7.7 million migrants of 1900-14 made up a bit less than 10% of the U.S. population then, but together with their descendants amounted to over 20% by the 1940s and over 30% by the 1990s. It is a reasonable assumption that today (2018) about one-third of Americans (probably something more than that) can trace ancestry to immigrants arriving from Europe during 1900-14 period.
It is routinely claimed that 40% of Americans in recent years are descended from arrivers at Ellis Island (operating most years from 1890-1930). Assuming that 40% figure is approximately accurate, it is thus a not much smaller percentage who are descended from migrants coming during just the peak years of 1900-1914 but to all four major east coast U.S. entry ports (New York, Boston, Philadelphia and Baltimore).
Note: This is a different question than that addressed here, "Immigrant ancestors and how they arrived." (What fraction of American immigrants who arrived between 1607-1914 came during the final 15 years?: Also, coincidentally, about 1/3.)
Business of Transatlantic Migration, p. 201
"Historical Statistics of the United States"
Tips for searching the Ellis Island database
This page last updated 15-April 2018