Exact symptoms you're describing occurred in my Mk4 (3 door) as result of poorly sealed rear side window following a repair. It started filling the rear footwell, then the level got sufficient to flood into the front footwell. Was a right pig of a job getting the underlay out to dry it as it was a one piece (until I cut it ssh it could be removed).
If you can rule out rear glass are the drain holes in your door clear? Or build up of leaves under bonnet and scuttle tray.
I'd be surprised if rubber mats would cause enough a build up under them. I've had rubber mats in my Mk5 for years and carpets are bone dry.
Good luck with the detective work