Hmm, there seem to be other threads about getting TinyTeX installed on a Windows machine. I am not a Windows user so I don't know that I can be helpful. Here are some threads that may have possible solutions for you:
- R knit to PDF not working properly with errors
- Can't install TinyTeX on Windows Server · Issue #327 · yihui/tinytex · GitHub
- Cannot install tinytex
Also, perhaps if we are lucky @cderv will appear. He is a wizard with these things.