After 1865, I’m thinking. That’s the usual given starting point for the truly massive immigration waves.
27 million people from 1865-1918, which was about the population of the UK in 1880. The US absorbed a whole Britain.
1865 was when Henry Bessemer hit on his process for consistently and scientifically making high-quality steel (or 1851, if you believe American William Kelly beat him to the punch).
Man had been making steel for more than 2000 years but that was more art than science, hit or miss. The Bessemer process (regardless who invented it) made it possible to make more-or-less 'perfect' steel on an industrial scale.
Which directly cause one of the greatest revolutions in the history of mankind. And according to his 'hockey stick' graph, the advent of industrial steel coincides very nicely with the start of the uptick (and it bore no allegiance to the invention of the lathe).