If genetic material did travel in either direction, it would be easily verified.
https://en.wikipedia.org/wiki/Timeline_of_the_far_future
is thought provoking.
1. ET life formed and vanished so quickly that they didn't even get to the stage where they generate electromagnetic signals.
2. ET life formed and got to generate EM waves, but:
- they're either too far from us that we haven't detected those waves yet;
- they only recently got to this stage and the signals they produce have not reached us yet;
- or both.
3. ET life formed way sooner than we did; figured out how to generate EM waves, and then vanished entirely. So, any signals of their civilization they must have sent out there have already reached earth, but before we began listening for such signals.
4. Then again, since there are practically infinite number of planets with habitable conditions for ET life, statistically speaking, we must have already received a signal from at least one of them.
Which leads me to this:
5. ET life doesn't exist, because the universe as we know it is most probably a simulation inside a computer and the computational resources can only render so many different objects at a time. (This is serious stuff, researchers have already proposed methods for verifying this: https://www.washington.edu/news/2012/12/10/do-we-live-in-a-c...).
Um, sorry to break it to you but the horse has left the barn in regards to future prospects.