If you only received your social security number last month then it is early to except to get anything else. Remember half of France is on holiday!
I think what you are expecting is the form that you fill in and add a photo to to get your carte vitale? I don’t know that you ever get a special card with your social security number on it - we didn’t.
More importantly have you received your attestation that you have been accepted into the health service? With that you can get everything that you would get with a carte vitale.
Go onto ameli.fr and you can find out where your local office is and contact details