To open a Cygwin terminal with 'the same' $PWD (more precisely, with $PWD_Cygwin = $(cygpath $PWD_Windows) as in Windows (e.g. your PowerShell terminal), simply do

C:\cygwin64\bin\mintty.exe -
cd "$(cygpath -u "$OLDPWD")"

in your Windows terminal/script/etc. The logic of the code follows from the fact that, upon initialisation (C:\cygwin64\bin\mintty.exe - ), Cygwin saves the old Windows $PWD as the Cygwin variable $OLDPWD (whilst setting its $PWD variable as /home/sh).

As an aside, we note the importance of starting Cygwin as a login shell: https://stackoverflow.com/a/43300782/31298396.