According to the Star Trek: Deep Space Nine Technical Manual, the Excelsior class has a standard crew complement of 750 units, between officers and regular crew.

Since the manual was written entirely from an in-universe point of view during the DS9 years (~2375), we can assume that this information could be considered up-to-date for the timeframe of the Dominion War.
Anyway, it should be noted that the DS9:TM has received criticism for some inaccuracies, especially in the section that describes the various starships, exactly what we are discussing here; in example, the Excelsior class is said to have a complement of 750 units, exactly the same of the much bigger Nebula class (that is more or less the same size of the Galaxy class); it seems a bit strange that these two very different ships could have the same crew numbers.