The first illegal aliens were the people who are now claiming “native” American status.
Illegal? That's a stretch. Anyway, we have our own history out here in California, less known than what is taught because the east coasters started the country as a nation.
Anyway, illegal aliens here could have been the Russians. They set up a colony just north of San Francisco (SF was known as Yerba Buena at the time). The Spanish were alarmed at the "invasion" of the Russians, and were preparing to do battle with them. A Russian ship came down from Fort Ross area and sailed in SF Bay. The Spanish cannons at the entrance didn't fire, and the Spanish met with the Russians. All the Russians wanted to do was trade and hunt, and agreements were worked out. Even some romantic intermingling went on. Russians eventually left, not interested at all in a conquest of California, and the Spanish got it all. History would have been drastically different if the Russians decided to stay and take SF.
One of the reasons the Spanish initially set up fortifications in SF (same time as the American Revolution was going on), was to stop English and Russian incursions into the area. Sir Francis Drake was an English pirate holing up in the SF Bay Area a couple centuries prior, but couldn't be called an illegal alien because Spain hadn't yet laid claim to California. But the Russians could be called illegals - maybe.