Could be leak-down in any portion of the oil system, from the drainback valve to the lifters, or the pump, or air added at shutdown with low oil level or foaming. Assuming it's a drainback or leak-down issue, or air in the system, a 10-second run with shutdown and restart would verify this (no rattle 2nd start). A filter change would (by probability) confirm if it's there. Disabling fuel/ignition for extended cranking to prime oil before start would confirm if it's in the lifters or pump. Measuring rocker/valve height on shutdown versus after overnight would point at the lifters, or intermittent would indicate specific lifters, and so on. One workaround if air/drainback could be a pre-oiler, pretty cheap with a fire extinguisher or propane body and a valve.
I had a similar one recently in a turbo-Diesel, and it was the filter valve, although it didn't completely solve the issue. I'm running some flush in the oil next week to see if a little cleaning helps the lifters. Yeah, it's pot-shot, but I'm not going inside the engine on this one.
I may do a pre-oiler this summer just to ease my irritation LOL.