No, it's not possible.
You're referring to PEOPLE, not exchanges. Sure, if you're buying bitcoin from an independent person you can use Paypal or any form of payment the seller accepts. But exchanges DO NOT accept Paypal. If I'm wrong, please list these exact exchanges. Thanks.
Great, it is possible. You need to sign up with an exchange and complete their identity verification procedures. Then you can link a bank account or credit card to the exchange and begin depositing USD or purchasing crypto currencies. The identity verification procedures are the same for nearly every exchange, however some exchanges are quicker to process those requests than others. E.g., Verification by Coinbase takes days.