Pushing back the evidence of life implies one of the following is true.
1) Life (abiogenesis) is easy to get started and the Universe is full of life.
Well, it shows that it is liklier easier than expected. If it took only a 300 million years to start here then the best guess at the mode is of course 300 million years, say down from 500 million.
That of course implies that the window for life to evolve is likely shorter than we previously expected and naturally the number of places with a short window must be greater than or equal to the number of places with a longer window (in any remotely statistically sane universe, greater).
As the minimum window shortens, the number of opportunities for life to get started expands.
I don't think that proves the universe is full of life.
2) It was an extremely rare event for life to start on Earth.
I don't see how it implies that. We don't know precisely how rare the event was but as the earliest point moves back, the event looks less rare than before.
I see things differently. I believe you are saying that since the time period is shorter, the probability for life must be greater. (Correct me if I am wrong.) I start with a fixed (but unknown) small probability. Then by shortening the time period one makes it less likely life would form, because there are less cases where the needed ideal conditions exist for life to form.
3) Life started somewhere else and ended up on Earth.
Not really sure how it implies that. No matter what the distribution of life seeds arriving from outside, the narrower the window, the smaller chance life had to arrive from the outside. So it implies this option is less likely, but not by how much.
4) Life had outside help in getting started.
You've just deferred the problem, though to whatever gave rise to the outside helper.
i.e. a supernatural event.
Possibly, but the probability increases from something minute to something marginally less minute. We've never seen any evidence of anything supernatural existing that's held up to scrutiny, so the chance of supernatural things existing is very small at this point.
Using that fixed probability and the shorten time period, I see the need to look for other opportunities, such as panspermia or a purposeful outside intervention (which may be a supernatural intervention). Personally I think there are enough stories of the supernatural miracles that you can not discount them. (One example is the rigorous process the Catholic Church goes through to verify miracles in their sainthood process. They have had atheists look at the evidence of a miracle to try to disprove it.)