If the iPad indicates that it must be restored, it already too late to recover anything from the iPad. All data and files locally stored on the devices have already been lost. If you have a pre-existing iCloud or iTunes backup of your iPad, this can be restored to your iPad after you have resolved the current problem. If you don't have a pre-existing backup as you describe, your locally stored data has been irretrievably lost.
If you see the Restore screen on your iPhone, iPad, or iPod touch - Apple Support
These support pages outline the available methods to restore an iPad - either from a backup, or to Factory Settings:
Restore your iPhone, iPad or iPod touch from a backup – Apple Support
Restore your iPhone, iPad or iPod to factory settings – Apple Support
Restore all content to iPad from a backup - Apple Support
You’ll need access to either a Windows PC (with iTunes for Windows installed) or a Mac (with iTunes or Finder - as appropriate for the installed version of macOS).
Download and use iTunes for Windows – Apple Support
Update to the latest version of iTunes – Apple Support
Use of a PC or Mac computer is unavoidable. If you don’t have access to a suitable computer of your own, that of a helpful friend or family member will suffice. Alternatively, the technicians at the Genius Bar of your local Apple Store or Apple Authorised Service Provider (AASP) will be delighted to assist.
Genius Bar Reservation and Apple Support Options - Apple
