2010 Ford F 150 Carpet is always wet under floor mat on driver side

If wet with no rain could be heater hose/core or A/C. Wet after rain a few links below.
https://www.youtube.com/watch?v=O6RaFLNrEDk
https://www.youtube.com/watch?v=IYivahDhgsQ
https://www.youtube.com/watch?v=Bw-PTAJtNvQ
https://www.youtube.com/watch?v=BctXRfLfeog

I feel for you as I have the same problem with my '92 GMC S-15, only on both sides. I thought it was the badly cracked windshield, only to have problem return in spite of windshield replacement. It would appear the problem is due to loss of foam/rubber blocks that edge the hood hinge openings on the firewall. I'm trying to figure out how to replace them at this time.

It could still be a leaking windshield and running under the carpet.
Or it could be a door gasket or one of the roof drains is plugged up.
You may need a body shop to check it out.

air con drain plugs blocked with dirt or muck, they are located under the car (2) on top of gear box.get under the landy and clean with a piece of wire.( hard to find).

Check under the carpet under the floor mat on the passenger side to see if it's wet you might have a leaky heater core if so just replace it and make sure the tubes are not rubbing against the body.

check under drivers side carpet under fuel pedal, there should be a small black hose which is supposed to run through a hole in the floor to the outside. This is a condensation drain tube. If it is not draining it will follow channels in floor to the back drv side floor well.

shop vac the carpet dry then spray garden hose around both rear doors or around doors and see if you get wet or see a leak. Also spray under vehicle on both sides of car and check for leak.

it is on the floor board just to the right of the trans hump pass side at upper edge of floor mat or carpet

did you drive in the rain before and this not happen. if you used the heater,or defrost,then sounds like heater core is leaking.

I am the original owner of camry xle 1998 with wet floors. In 2000 I had drivers side door seal leaking at welt. Removed old door seal and new weather strip on drivers side installed. The door panel was never wet, but wet at bottom of door where there are drain holes...slowly leaking under carpet.
In 2001 later water again. Coming from overflowing A/C evaporator-drain plugged/ tank full of debris. Removed evaporator, cleaned + drain cleaned.
In 2003, driver door seal against window rotted. Removed door panel and found leak at window belt molding at the mirror joint inside + out. Lots of mold under carpet needed to replace! Made a fuss at dealers for reacurring problem and they replaced the carpet for free.