I have had this problem on an engine and found that knock caused by a camshaft plunger and spring problem will occur all the time, not just at start-up.
I also think it may be due to loose main bearings or if it is a babbet engine, incorrect groves or "reservoirs" in the main bearing babbet that allows all the oil to drain from the valve chamber after the engine is shut off. It takes a little time for the oil pump to re-fill the valve chamber and once again get oil to the mains.
I always add 1/2 bottle of STP to my oil, it really CLINGS & helps on a "DRY" bearing start.
Mitch will probably LECTURE me, save your ENERGY, Son!!

SA Dad