It's too late to backup now. You have to restore your iPad. You will lose everything on the device. Having an iTunes account has nothing at all to do with any of this. Besides, I think that you mean that have ever synced with iTunes. And once again, it doesn't matter. You still have to restore the device using iTunes.
There is no other option - that is if you want to use your iPad again, there is no other option.
Read this for more information and for the instructions. There are several ways to restore your iPad, you can use any computer that is running iTunes, if you do not have a computer of your own.
You will be able to download most of your paid content again as well, if you have no backup and I think we have established that you do not have one.Take a look at this.
If you can’t update or restore your iOS device
iPad Stuck in Recovery Mode after Update
You can use iTunes to exit recovery mode.
(1) Connect your iPad mini to your computer and run iTunes on your computer.
(2) Select your iPad from the list of buttons at the top of iTunes, then click the "Restore" button.
(3) Wait for the backup and restore process to complete, then "restore from backup" in iTunes after the phone has been restored.
Read Apple support for more details:
NOTE: This method will fix iPad stuck in recovery mode, but will restore the iPad in the process. This will erase everything on the iPad, but a backup will be created during the Restore process, allowing you to recover your data.