I had to take another look at where you were from, MMitsock, because I could understand if you were from SoCal or the southwest...we don't get rain very often

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Is this something the dealer could cover under warranty, or is your basic warranty expired? I wonder if it would be covered anyway since a Toyota dealer didn't perform the services...whatever!
Another option may be to call the place that installed the windshield. Most places cover their install and products for a long time, if not for the 'lifetime' of the car...minus normal wear and tear and stonechips and baseballs and ...you get my point.
Like Yitbos said, I would pull the carpeting and dry it before mold/mildew ruins it completely. There shouldn't be any holes in the Tundra cab that would allow water in, at least I wouldn't think so! Have you drilled thru the floorboards for any wiring or mods that you can think of?
Just posting my thoughts to try and offer help!
Andy