Some people have proposed resetting year 1 to 10,000 years earlier. The current year would be 12024. This way you can have pretty much all of recoded human history in positive dates, while still remaining mostly compatible with the current system. It would certainly be convenient, but I don't expect significant uptick any time soon.

For earlier dates "n years ago" is usually easier, e.g. "The first humans migrated to Australia approximately 50,000 years ago".