Restore ipad without touchpad

When you say the touchpad, are you referring to the touchscreen? You’re unable to use the touchscreen for set up?

If I’m understanding the issue correctly, yes you can use iTunes to restore a backup.

Restore your iPhone, iPad, or iPod touch from a backup - Apple Support

If your previous Bluetooth/mouse settings were backed up you may be able to restore the backup from your computer using the above article.

Note: you'll use iTunes if you're using a windows computer or old Mac and Finder if you're using an up-to-date Mac.

Depending on the iPad you're using you may be able to get something like: Magic Keyboard for iPad Pro 11-inch (3rd generation) and iPad Air (5th generation) - US English - White - Apple

Obviously you'd get the model that's compatible with your iPad, that's just an example. But those accessories should work during setup.

Again depending on your model, if you have a base price model or old model, and if you don't have AppleCare+, it may be more cost effective to replace the iPad than to repair the touch screen or to buy an expensive accessory.

If you're unsure of what repair options are available Contact Apple for support and service - Apple Support

I, unfortunately, can't test this without erasing my personal iPad. But it should work just like plugging a keyboard into a PC. It transfers data using the magnets on the back of the device, and should therefore work like any plugged-in input device.

Double check with the retailer, but if it doesn't work you should have a return window. Usually 14 days.