I mean sure, a long standing heater core leak can rust out the firewall.
But given the OP’s description of where the water is and the fact that it’s a ‘73 Duster, well, I think @Professor Fate covered it.
On my ‘74 Duster I had 3 out of 4, the wiper pivots leaked, the cowl drains were plugged and there was a windshield seal leak too. All of which put water exactly where the OP described.
The cowl drains are big one, all the stuff on the floor in this picture came out of the cowl on my car…
Fortunately being a California car all that junk didn’t rust out the lower cowl.