Why is my Panasonic Whisper series bath fan starting up so slowly?
To make these fans quieter, the fans are designed to not create as much turbulence, which means they "slip" more when the air is not moving already, i.e. when you first turn them on. In addition the Panasonic fans have a built-in damper that prevents the cold air from flowing back into the room when the fan is off, so before it can move air it must get that damper to open, and when it is just starting there is not enough air pressure yet to open that damper. All of that can give you the impression that they are not yet working, but they are. This is likely just something you need to learn to live with, i.e. turn the fan on as soon as you enter and maybe use a timer to have it run on a while after you leave.

That said, there are a couple of things to check;


Assuming this was a retrofit? If so, did the old fan system have a damper somewhere else in the air duct, like at the vent hood at the very end where it comes out of the outside wall? If so, then your poor little fan has to open TWO dampers. In that case, get rid of one of them.
Is the vent pipe too long or has too many bends in it? If so, is there a way to shorten / straighten it? If not then you again may have to just live with it.
Is there a proper vent pipe at all? Some unscrupulous types will just dump the air into the attic area and there may be an obstruction or insulation blocking the air flow. if there is no vent pipe, it may be a code violation and your HVAC contractor should correct it.
Do you have proper "make up" air flow coming into the bathroom? A common mistake is that people have no grill on the door and then have thick carpet coming right up to the door, so that air cannot get through the crack in the bottom. When a vent fan pulls air OUT of the room, air (from the rest of the house) must be able to get back IN to make up for it, those little fans can't pull a vacuum. So if there is no way for the air to get into that bathroom, or even (in extreme cases) the house is sealed up so tight that NO air gets in ANYWHERE, the fan has to struggle to get anything moving.