I think a shuttle is 500m3 when repackaged. Do you have a t1 hauler? If you do and still don’t have enough room, try putting a “cargo expander” on it, should fit then.
if you are in the correct station, double check that you have the correct item (exact spelling, exact name, close enough is not close enough.) Make sure it is repackaged and has a 1 in the corner of its icon. Make sure you are in the exact correct station, not just the system but station, check the spelling letter by letter. If you have to move the shuttle somewhere, assesmble it, fly it, then repackage it, no need for a hauler, it has engines on it.
edit: you can check a mission progress by opening up the journal (alt j) and double clicking on the mission. Look for whatever has a yellow circle instead of a green check. Also double check that you even accepted the mission.