Another telltale heater core leak clue: Front windshield likes to fog up at startup after sitting a while, enough time for sufficient leaking coolant to vaporize on the surface of the heater core as it heats up and steam up the windshield.
However---
the #1 reason by far for wet carpets up front is leaking blockoff covers over the vestegial foot vents behind the plastic kick panels. By far.
Open up the kick panels, pour a good quantity of water into the windshield cowl louvers, and watch with a strong light for the small rivulets of water emerging from the corners of the rounded square plastic blockoff plugs. Clean well with brush and detergent rag, dry, and seal it up with good body seam sealer or butyl caulking, or contractors grade caulking. Silicone caulk or most other water-based products don't seam to stick well over time.
Second (or third) most common reason for wet front carpets (in competition with clogged sunroof drain tubes) is mis-positioned baffle diverter cover over the wiper motor under the windshield cowl. Allows water to enter thru the HVAC fan housing, and will also degrade the lower fan motor bearing. This will drain into that side footwell only.
Other places to look for leaking coolant, in descending order:
1. Heater flange o-ring seals at (1.) rear of cylinder head and (2.) rear of engine block (mentioned above). You will see coolant dripping off the bellhousing.
2. Leaky hoses
anywhere, could be pinholes or seeping thru clamped areas.
3. Heater core or Radiator.
4. Head gasket (external leak) look under the vacuum pump for the most common location.
5. Plastic drain tee above the oil pressure sensor/motor mount bracket area.
Some of these coolant leaks I believe are self-induced as Volvo fitted a higher pressure coolant cap as a standard "feature,"
overly stressing especially the heater core and radiator. The black ones (75 kPa?) are safer.