It is a confusing sentence. It means something like, "Do you remember meeting your best friend for the first time? Could you ever forget that?" Meaning that, " don't we all remember that first meeting?"

Olga, I am sorry to say that no native speaker who purports to know how to write English would write that. I think possible ways of saying what you want to say may include: Do you remember how you met your best friend? (This already implies "for the first time") Have you already forgotten how you met? In your sentence, even if you leave the"ever" out, it is wrong and does not mean anything. "Have you forgotten xxxxing...?" is not a correct structure to use. It is never used, regardless of what you want to say.

Another possible way of saying this sentence might be: Have you ever forgotten when you met your best friend for the first time?