It's one of the deadliest yet most common mistakes to make for sure.
By using their service, you are agreeing to a bunch of terms and conditions which do not hold them accountable. It is also clearly stated that you are depositing to a USDT address before you are able to generate one:
While you can try to convince them that they have the moral obligation to refund you the funds, it is true that it takes manual labour to get this done, and if they handled every case that came their way there's probably going to be major disruptions, especially for smaller amounts.
I wish you good luck, but I can't honestly see anything other than an automated reply from them with the same message every time unless you get lucky.