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Let's say the Gap ended roughly 300 years ago. (I get the impression this is the right general range from what's been leaked so far, but I'm really just pulling a number out of the air.) What do you suppose we see when we look 300 light-years away from wherever we are? Does the Gap comprise an effective limit on the visible universe at the appropriate range, based on X light-years since the Gap ended?
In theory, we'd be able to look past it to the other side of the Gap, but then we'd know how long the Gap lasted... not to mention the weirdness of being able to see things 3000 ly away and 300 ly away, but nothing in between.
I think that a lot depends on what you can actually see from such distances. Generally, if their telescopes are as good as ours, they could immediately locate any given star/sun and, with sufficient observation time, identify the orbits of its major planets. For most solar systems, that information would be of trivial importance, as all major planets would be where you expect them to be from extrapolating their orbits backwards.
The single exception, of course, would be Golarion itself. Unless some phenomenon blocks the view of Golarion's solar system from outside, it would be possible for starfarers to work out exactly when Golarion disappeared -- and as I recall, that is something that is supposed to be unknowable.
If the length of the Gap is also supposed to be unknowable, it would be important to ensure that no accurate astronomical records survive from before the Gap. Otherwise, astronomers in the Starfinder era would be able to extrapolate planetary positions backwards so as to be able to match up a known pre-Gap date with an exact duration before the present -- and with that information, a very close approximation of the duration of the Gap (from latest known pre-Gap date to earliest known post-Gap date) could be calculated.
This assumes The Gap Censors (the gods or whoever) won't apply Gap censorship to all forms of EM radiation that has come from or been reflected off Golarion for the duration of its existence. It might be as though Golarion never existed.
But this does not completely solve the issue. Golarion as a planetary mass has a pull of gravity on every other planet, even the sun itself. Sophisticated enough instruments should be able to analyze the motions of the rest of the Golarian system, against what it's supposed to look like, and then use fancy math to compute when the gravity well of Golarion disappeared. The Gap Censors would have to expunge all pre-Gap astronomic records of the Golarion system so there would be no control data to compare to.
Maybe all light coming from Golarion disappeared along with it.
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One solution for the gravity problem could simply be that Golarion's gravitational influence is still there, even though the planet is missing. We are dealing with hefty magic anyway. If you fly there you find nothing, but all the other local bodies move as if the planet were there.
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See, I'm actually kind of more interested in the other end. Obviously, using the Drift to jump 300 ly out and then look back at Golarion would be one way to try to "solve" the mystery of where the planet went, but consider this: without other deific shenanigans, right after the Gap ended, there would have been no stars in anyone's night sky, a state of affairs that would have lasted years. It would be decades before there were more than a tiny handful visible from a typical planetary surface, and even three hundred years later, space would look a whole lot more empty than it does now.
The Gap looks more like a planned effort to remove memories and records of events than the elimination of light already emitted from various astronomical bodies. We also cannot assume that the time that the loss of memory and records occurred and the end of the Gap are the same time -- it is quite possible, for example, that the loss occurred 50+ years after the end of the Gap, with only selective incidents that would provide evidence about events during the Gap removed from later memories.
Since the elimination of all light emitted by heavenly bodies during the Gap would provide more information than it would conceal, I would assume that that didn't happen and that people living immediately after the establishment of the Gap could still see a full night sky.
I think the extinguishment of light would only 'black out' light from the Golarion system, and nothing else. This would be the light sphere from Golarion's sun (and the reflected light from its planetary disk) out to a radius of 4ish billion light-years.
Instruments might be sensitive enough to compute the Golarian system's gravitational effects on other stars that swing close by. However, the contribution of one terrestrial planet would be miniscule in its path of orbit around the dominant mass of the star system.
The precision required to measure distances between stars and planets light years apart, to within even thousands of miles, would be a daunting task.
it is probable that the gravitational waves from Golarion's star system (interactions between the star and its planets, and between one planet and the others another) is masked too.
Trying to extrapolate when Golarion's gravity well ceased to influence nearby stars could be well beyond the ability of even Starfinder's computers.