There are two different scenarios in your question and I'm not sure which you're asking about so I'll answer them both.
- You want an accurate map that shows the "current" location of everything in the galaxy
And you have tracking beacons attached to everything to aid you with this. This is only possible if these tracking beacons can communicate using your ftl-travel method, if they were limited to the speed of causality there is no way they could communicate a change in location instantly to someone lightyears away.
There is one exception to this. If you ignore the potential changes resulting from randomness (in quantum mechanics there is true randomness and it can affect macroscopic environments as well, as proven by the simple fact that we can observe such randomness and act on it), you could, given a very powerful conputer, calculate the current position of everything based on a one-time shot of the universe. In this case the humans who go around attaching tracking beacons to everything could just record its position, speed, direction etc. and start the simulation once they gathered enough information (they might have to initialize it to account for different objects being recorded at different times, but this shouldn't be a problem so long as they make sure they there were no interactions between two objects while one was recorded and the other wasn't).
This simulation could either be run on a central computer which has to communicate through ftl-based methods with every client or run on every client in a manner that completely avoids ftl communication but requires every new client to wait until the nearest existing client can send it the current state of the universe.
- You want a map that shows not what is, but of what can be seen
This would mean that the map would be different for every client but accurately represent the current state of the universe as seen from that point. On this map you could still see a star 5000 lightyears away even if it actually went supernova 3000 years ago.
This is fairly easy to accomplish and requires no ftl communication but requires you to wait a while if you want data about faraway systems.
You can do this by placing a tracking beacon on everything and just have it broadcast its position. Assuming communication methods which travel at the same speed as light this will cause the relevant data to arrive exactly when the object can be seen as described.
Of course, if an object is 4000 light years away but the tracking beacon was only installed 2000 years ago that mean you're not yet receiving any data. To counteract this you could combine this method with the "simulation" method described above to have a (backwards) simulation bridge the timespan between installment of transmitter and first transmission receival. This would require the simulation to be run on every client or the central computer to generate a new universe state for every map request.