Normally, YVR is a preclearance airport, but due to the late timing of the YVR-ATL redeye, and the fact that US CBP at YVR closes at 8 PM, YVR will leave from the normal international area at YVR, not the US preclearance area. Thus, when the OP arrives in ATL, they'll have to go through customs & immigration at ATL. It doesn't matter if they show up before US CBP closes at YVR; DL isn't going to segregate the arriving plane into people who precleared at YVR and people who didn't.

Back to the original question...IME, at 6 AM, it doesn't take long to get through customs & immigration at ATL. What you'll do is get off the plane, follow the signs for connecting flights, and an immigration officer will check your passport to make sure you're eligible to enter the US. Once through that, you'll have to pick up your checked bag (if you checked one) and go through the customs area. Then you'll drop off that bag at a special belt (again, if applicable) and clear standard US-style security to enter ATL terminal E or F. From there, take the plane train to the concourse of where your second flight leaves from.