Where in the digestion system do pepsin and hydrochloric acid begin the splitting of the proteins?

In the Stomach.

The first part of digestion is chewing in the mouth and mixing with saliva.

Then swallowing.

THen when in the stomach, the stomach walls naturally secrete hydrochloric acid and pepsin into the 'mix'. The stomach operates at pH = 1. This is a natural process, and you DO NOT swallow hydrochloric acid.