They would tell you that you need to talk to billing, and billing would tell you they can't provide pricing at all and they can only tell you after going through your insurance, or they would require a zillion digit billing code that only your doctors can provide, and your doctors are not going to waste their time giving you the list of a thousand codes for whatever operation you're doing, or at least not accurately.

In short there is no way. Either you accept treatment and you're billed what you're billed and you hope insurance only fucks you over a little bit, or you're denied any service short of immediate life saving.