Information theory 101: Either you know something, or you don't.
The map can be falsified (proved false) if it describes something physically impossible or extremely improbable. However, a sufficiently motivated forger can avoid this by running physical simulations of the map and verifying that it is physically stable over the short-to-intermediate term (which is exactly what you would do to check for these physical impossibilities in the first place).
Otherwise, it's a matter of comparing the map to reality. The problem with that is twofold:
- Some aspects of reality are already known, to both you and any sufficiently well-motivated forger. Because you already know these things, a genuine map tells you nothing interesting about them, and a good forgery will contain them anyway.
- Some aspects of reality are unknown, to both you and any forger. Because you do not know these things, you cannot use them to verify the map.
If you need to know whether the map is real based on the same set of information as the forger has, you are out of luck.
You could wait for more aspects of reality to become known (i.e. for more stars and exoplanets to be discovered), or perhaps use nonpublic information depending on who you work for (e.g. the military?), but the above dilemma continues to hold: Everything which is learned is now known, so the map can no longer provide new information about it. And that's assuming that science follows a straight line from unknown to truth without passing through falsehood, which is unrealistic. It would perhaps be more accurate to say that there is a continuum between (1) and (2), and it's often difficult to know exactly where you are on that continuum. It's possible that a genuine map might disagree even with supposed "known facts," if our understanding is badly incorrect.
Perhaps, after enough new stars and exoplanets have been discovered, and the map has agreed with these discoveries sufficiently often, you will conclude that the map is genuine, rejecting the possibility that a forger managed to guess all those discoveries by chance alone. But how often is "sufficiently often" and how many discoveries does this take?
To answer that, we (usually*) use statistical significance testing. Basically, you imagine (or simulate) numerous forgers creating numerous fake maps, and try to figure out what fraction of those fakes happen to look at least as realistic as the map you actually have. If this number (called the p-value) is very small, you can argue that it's unreasonable to continue believing the map is a forgery. Your definition of "very small" (the significance level) will depend on what (if anything) you plan to do with the map once you know it's genuine. If you're going to launch a generation ship at an exoplanet, you will probably be a lot more cautious than if you're going to point a space telescope at an interesting area of the sky for a few days. If you don't plan on doing anything in particular with the map, perhaps you should ask yourself why you care about its accuracy in the first place. That reason will inform your choice of significance level.
If all that is a bit hard to follow, here's the short version: You can wait for some more celestial bodies to be discovered by astronomers, compare the newly-discovered objects to those in the map, and use that to prove the map is (probably) real. But if you do that, you won't be able to use the map right away, and by the time you are able to use it, it will be partially redundant to the newly-discovered information.
* This link included for completeness; you can completely ignore it if it doesn't make sense to you.