It is said that tar is included with Windows 10:
www.andysblog.de
tar does not transfer files. It is only an archiver. But you don't need to check if the transfer is being done timestamp-aware because you don't transfer the single files and folders, only an archive. If the archive does not keep timestamp when getting transferred, it does not harm. tar should be an easy helper for what you want to achieve.
On my Android device tar is directly available when called in a terminal.
If you want some GUI, so you don't need to use the command line, you will most probable need to download some archiver helper. Guess 7zip GUI will be fine for creating and extracting tar on Windows.