I just got denied an AMEX blue credit card , when can I reply apply

I just got employed and was rejected for my Amex blue credit card in the US. The reason being insufficient proof of deposits as compared to my annual income.

I put in my annual income but I’ve literally been employed only for few days and haven’t received my first pay check. Maybe that’s why.

It said applying won’t affect my credit score. But I got denied, does it affect my credit score?

Also when can I reapply so as to not affect my credit score if I get rejected?