Hi,
In the months since first posting on this thread I've purchased a 1st. generation iPad running iOS 5.1.1 myself. I've been able to get it fully connected up to iCloud (including Find My iPad, my iCloud email and all the other bits you'd expect to work under iOS 5.x), as well as iMessage, Game Centre and so on and so forth. The trick is, as a previous poster on this thread rightly stated, to try to log in once. You'll get an error. At that point (assuming you have some kind of 2FA enabled) you'll get a 2FA prompt on your "main" iOS device, and you can then approve the login and you'll be given a six-digit code. You then append that six-digit code to your password and try to log in on the 1st. generation iPad again.
So, for example, the order of events might be:
1. Try to sign in to iCloud on the 1st. generation iPad with your password, which for the sake of argument we'll say is "letmein".
2. It won't work, and you'll then get a message indicating your sign in failed.
3. At the same time, on your main iOS device running iOS 9/10/11 with 2FA enabled on your account, you'll get the "Someone tried to sign in to your account" pop-up. Choose "Allow" as an option.
4. You're then given a six-digit code to use on the new device. For example here we'll say the code you're given is 123456.
5. On the 1st. generation iPad, try signing in again, only this time use the password "letmein123456".
6. Your 1st. generation iPad sould now sign in to the iCloud serivce you were trying to use.
7. Repeat steps 1 through 6 for every iCloud service you need to sign in to on the 1st. generation iPad.
Hope this helps. If it doesn't, try creating an application-specific password in your Apple ID management page and using that instead. You'll probably have to create an application-specific password for each and every service you need to use though (i.e. iCloud itself, your e-mail, iMessage, Game Centre, etc), so hopefully the above method will work for you.