There are ways to determine it without needing a time machine, though it is difficult. While you can't really disprove panspermia, one way to demonstrate it's truth (if it is true) is to find an asteroid or comet or other fragment bearing life or proto-life that is basal to all life on Earth (ie, once establishing it's relation to Earth life, ruling out the possibility that it originated here).
Panspermia, while unproven, is a legitimate hypothesis as a part of the history of life on (and off) Earth, but it is not a solution to the origin of life itself.
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