Hi ,
I'm Dyari. Thanks for reaching out. I will be happy to assist you in this regard.
You’re right that during Windows 10 installation, it usually asks for a product key, but you don’t actually need the product key to install Windows. When the screen appears asking for the key, there is an option “I don’t have a product key” or “Skip for now”. If you click that, Windows will continue installing normally.
However, after installation, Windows will run in an unactivated mode. You can activate it later if you find or buy a new key.
About finding the old product key, if you no longer have the box, email, or receipt, there’s usually no way to recover it from the USB itself. Microsoft does not store it on the flash drive. However, if you can contact the vendor or shop where you purchased it, they may have a record of the product key.