A calendar is a tool for measuring and subdividing time. Its components (such as Days, Months and Years) are just convenient packages of time. They assist calendar users in equating the passage of time to recognizable spans within their own lifetimes.
So ignoring the packaging, a calendar only needs two components. A starting point and a unit of measure. For the calendar to work across the entire galaxy, both of those components need to be absolute and immutable across all time and space.
I would propose that measuring every moment in time as its distance from the instant of the big bang, in units of atomic seconds where...
the official definition of a second is 9,192,631,770 cycles of the
radiation that gets an atom of cesium to vibrate between two energy
(We might round that cycle count up to an even 10 billion just to make the math easier, but the rest of this answer assumes that we leave it the way it is stated above)
How we determine the exact instance of the big bang is probably beyond our current science, but hopefully we will figure that part out by the time we colonize the stars.
As for making such a system usable to "people", we would probably create new convenient packages for day to day use. A
CentiSecond HectoSecond for 100 seconds could replace the minute. A KiloSec would then be about 16.667 of our minutes, so 4 of them could replace our hours. A MegaSec is only 277.778 of our hours, so that would be close enough to replace our weeks. In fact, it's 11.574 days the equivalent of our fortnight. And with adequate advancements in medicine, average human lifespans might someday reach 10 GigaSecs.