I arrive at Beijing Capital Airport from Detroit, MI at 2:45pm (on Delta Airlines).

It's international to domestic transfer in T2. And yes, Health & Quarantine and Border Inspection are necessary. Generally speaking, you need at least 2 hours to make this connection.
The correct procedures are the following:
Health & Quarantine → Border Inspection → Go through the Entry Frontier Inspection → go to the International Baggage Claim Hall → Customs Inspection→ Finish domestic flights transfer procedures & deliver baggage → Domestic Security Inspection →Waiting & Boarding
Good luck!