The estimated usage or 'level billing' programs, at least here, are based on 12 months prior usage data. They average your charges so you get the same bill each month. I never use any such programs; I'm ok with $15 bills in the summer and $60 bills in the winter.
I pay electronically too but they still send me a paper bill and you can log into your account to see the current charges. If you've been paying electronically, there should be a way for you to see a billing history. If they say the gas meter hasn't been working but you were paying something, it could be that you've only been paying the 'delivery charge'. You'd be able to see if that were the case with the billing history because your bills would all be the same and would be very low.
I don't see how they can force you to use an average method if they truly don't have prior usage history for you. They can't just make up an arbitrary number. You could offer to pay monthly for some period and have them use that average to bill you for the last year where you supposedly weren't paying for gas. And of course if they agree to that, conserve gas as much as possible to keep the bill down.
Good luck.