Can I bypass the verification process when trying to buy ETH via Ramp?

You can't. This might seem like a hassle but consider it a great security measure that will work towards your benefit as well. After completing the verification process, you still have to wait for the Ramp team to complete the process on their end.

This step will vary, and may take around several up to a few hours. Once the verification is completed, you’ll receive an email instructing you to complete the transaction.