There would be no other solution. Other than, as I said, seeing if they are on your card, phone, or in the account, and checking the phones settings to see that it set to show contacts from all sources. If it isn't, then I would set it to show them from all. If it is, or after you change it to show from all, and they don't show, they are sadly probably gone.
The only other, and this is only a extremely rare possibility that it would help, option that I can think of is to try one of the recovery softwares out there. They are usually free to try, and will search the phone to see if they can find any files at all. However, most of them charge a fee to access any recovered data. And there is no guarantee this would work.
Those are the only options.
In the future I really suggest backing up all info to a computer or cloud account. You can do that with contacts. I save mine to my computer, and make hard copies as well.
Good luck.