Your numbers are off, and you omitted emigration numbers.
https://www.census.gov/popclock/ says
> The United States population on January 1, 2019 was: 329,474,910
> The United States population on December 31, 2019 was: 331,163,242
Difference = 1,688,332
(Your given population numbers correspond to roughly October 4, 2017 and May 4, 2018.)
Your 1.03M appears correct - https://www.dhs.gov/immigration-statistics/yearbook/2019/tab... . It's the 3rd smallest number of the most recent 15 years. Smaller also than 1906, 1907, 1910, 1913 and 1914.
However, people do move away from the US. https://www.census.gov/library/stories/2019/12/net-internati... comments "Net international migration added 595,000 to the U.S. population between 2018 and 2019, the lowest level this decade."
Thus, it does not appear true that "The American population increase is entirely driven by immigration".