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Stuart_Armstrong comments on The Octopus, the Dolphin and Us: a Great Filter tale - Less Wrong
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Depends on the hypothesis. We have some pretty good picture about the development of the Milky Way. If your theory was about rates of supernovas or a certain proportion of heavy metals, then we could check whether those happened recently. If it was more specifically about Earth-like planets, we could record the hypothesis, and check it in a few years or decades as our picture of Earth-like planets around other stars gets clearer.
Silly me.
"Suppose I had a hypothesis that all Earth-era and earlier planets shared some feature that some later planets don't."
Given that we don't know what the requirements are to be a galactic phenomenon, figuring out which one we don't have is impossible.
Then we can do the reverse approach - crush all the data we do know, and see what changed about the time our Earth came around. We can then take all these candidates, and check whether any seem plausible, then do some further investigation.
While not logically impossible, a test that requires an astronomical amount of time to attempt is not something I can update on.
That said, there is a fairly low prior that the conditions for a galactic civilization to develop in the current era are better than they were last era. There is, however, quite a bit of evidence that there is not currently a galactic civilization.