Anything intelligence enough to find us, or be putting out signals we can find with instructions on how we can reply in a reasonable number of human lifetimes, is intelligent enough to stay well hidden for us lest we infect them with our stupidity!

"Sometimes I think the surest sign that intelligent life exists elsewhere in the universe is that none of it has to contact us"

-Bill Watterson (via Calvin & Hobbes)

Maybe they need to invent a time machine to start getting immigrants from different time periods?

Slightly tangential: there's an excellent Norwegian TV series based on the premise of suddenly appearing immigrants from earlier time periods, see https://en.wikipedia.org/wiki/Beforeigners.

and a south park episode for ones from the future :D

https://en.wikipedia.org/wiki/Goobacks