Hi,
I will run you through some quick ideas as it’s late for me.

I wouldn’t say unfortunately you don’t have a sun roof.
I have one in my 1991 sedan and never use it that often.
Maybe I’m too old but when you don’t have too much hair a hat doesn’t need that much airing out.
No hair mean no oil is needed so then no accumulation of that is going on. (:-)

It’s very possible that you have a leaking windshield due to rust under the gasket, if it has ever been changed out from the original windshield?

The next thing is to look under the dashboard behind the glove box.
Up above the electronics mounted there is the place where the wiper motor comes through the firewall.
There is a large rubber grommet right there that does shrink over time, from what I have read.

Also if, the wiper motor has been removed for replacement or repair, that seal will get disturbed.
It will not be pliable enough to reuse again without adding sealant.
Duct seal from a hardware store can be used instead of messy silicone.
It’s cheaper and is not hygroscopic as many silicones are. Those can promote rust and since you are in a snow belt region, where salt might be used, you don’t need that!

Look to see if any dust has been rinsed away in a trail going downwards from up high.
Hose down around the windshield mostly first and see if the water seeps in.

When the hood is closed it is less likely to let water in the wiper motor mount location but is not immune or fool proof.
You might want to put some paper towels up above the electronics, temporarily, for sure. Look for something that get dampened.
You don’t want water getting into the ECU or the system relay tied around there.

A Water puddle on the top of mat means it travel outward from the firewall and possibly on duct work.
Water beneath a carpet means it ran down the slope from the firewall.

If the car has AC there is a rubber boot that is supposed to seal both lines going to the evaporator.
Check its integrity.

If it was summer time or you run defrost in winter, an awful lot, then it could be condensation.
It’s possible that the rubber duck bill device that drains, the catch pan, is plugged up.
You have to remove the console side panel and feel under the pan to give a squeeze or go under the car to reach it above the transmission.

Now for the scary part and that is a coolant leak.
So make sure it’s just plain water in the combination foam/rubber mat under the carpet.
Hope it doesn’t smell or feel like antifreeze.
If the inside of a windshield gets an oily film on it that smears while cleaning, not good!

Let’s know what you find.
Good night.

Phil