Is it true if i apply for a credit card and get rejected, my credit score will be lowered?

I want to apply for an American Express Blue Cash card. I’m 21 and I don’t know my credit score as of right now. I have one credit card right now with 0 balance from Bank of America. Should I apply for the AMEX card?

How do I get a student credit card with no credit?

Everybody told me I’d get accepted for American Express Blue for Students because they LOVE to give cards to ANYONE, but I was rejected. I have no credit. What are some other student cards that might accept me? If I get rejected for one card, does that mean the rest will reject me too?