$12,000? A lot of banks wouldn’t be able to cover that easily without a day’s notice. I pulled out a couple thousand during the 2008 banking troubles and they had to get a manager to open the little safe under the tellers’ work desks because it was more than the drawers had. And cash has become less used since then.
$12,000 shouldn’t be a stretch for any reasonable bank branch. However, you’re correct that you normally have to pre-order cash in large amounts (e.g., $50k), as branches normally place regular cash orders to satisfy commercial customers and having someone pop up and ask for an unexpected $50k can be difficult to handle otherwise.