Well, technically, they get notionally assigned very early on (hence seat maps being available at the time bookings open), but those assignments are then "fluid" and can change repeatedly. Assignments then become publicised in the last two days (and thus become visible on Flightradar24 and the likes), but they can still change literally till the plane departs. For instance, if the planned plane is arriving late and there is a spare, assignments can change in just before boarding, and of course, if a plane goes tech, the assignment can change after boarding too!