Yes. There are two ways you can buy cryptos for USD, EUR or any other fiat currency.
1. Use Fiat exchanges. In these exchanges you can deposit fiat money using your credit card, bank account, or any other payment method.
2. Use quick buy method. Most of the exchanges that don't offer fiat deposit option offer you the chance to buy crypto directly using your credit card or bank account. Not that in case of this type of direct buy option fiat money never lands your account.