If you prefer sideloading using a computer and tools like Sideloadly or AltStore (though AltStore typically requires iOS 12+), you can find archived IPA files.
: If you haven't "purchased" it before, sign into your Apple ID on a newer device, "buy" the free YouTube app there, then return to your iOS 10.3.4 device to see it in your purchase history.
: Use a tool like h3lix (common for iOS 10.3.4).
: Open Cydia and download the Filza File Manager .