Your post makes the USA sound like it was an open country nobody was ever questioned or detained or repatriated due to a lack of passport or credential. This was not an open country ever.
Wrongo. The present passport system did not develop till after WWI, and the US did not fully enter into the system till just before WWII.
As far as I know there were few if any deportations from the USA until the 20th century. The few laws in place earlier were focused on preventing entry of individuals meeting certain criteria, not removing them once they were in the country.
The US did not even begin collecting records on immigration till the 1820s and records were sparse and incomplete for a long time after that. Nobody cared much.
If your claim is correct, you should have no trouble providing documentation about restrictions on immigration in the 18th and 19th centuries.