Humans introducing themselves to areas outside of Africa.

Although, this depends somewhat on your definition of "humanity", as there were several times in pre-history when hominids seem to have migrated out of Africa. If you mean "anatomically modern humans", or "homo sapiens sapiens" then this would be circa 100,000 years ago (although various pre-homo sapiens hominids had migrated out of Africa previously).

At the time when homo sapiens sapiens migrated out of Africa they seem to have had no domesticated animals, and had not adopted agriculture, so they would not have introduced any new animals or plants to new areas.

Other than themselves as an invasive species, they may have introduced their own parasites, and possibly (though less likely, due to sparse populations) some diseases.

Until something older comes along, I'm voting Dingo, arriving 4500-18300 yrs ago in Australia link. This deserves an asterisk because (1) the date range is determined by dna testing rather than some written record, (2) there appears to be some debate as to whether it came with us on a boat or wandered over from New Guinea when it had a land bridge and people had been in Australia for ~20k years.

Also, I would quibble with humanity outside of Africa being invasive. IF we had been placed somewhere by a higher species, and that Aliens dude on the History Channel was right all along, only then would we be invasive. If any other species gets somewhere on its own, then thrives, that's its native habitat.