That sound is coming from the valve train. With the springs exerting pressure on the valves at different times it is hard to see. Remove the valve cover and first check to ensure that oil is indeed being pumped to the valve train. The valve stems and rocker arms should be wet with oil. Next, turn the crank to compresson for cylinder 1 and feel the rockers for looseness. They should move sideways on the lifter shaft. Then try rocking them up and down to check for vertical play. Check the gaps. It could be that one of the "buttons" that go on the valve tips has fallen off; that would cause a large gap and increased
noise. (yes you will feel a pulsation from the decomp lever because it is interacting with the moving valvetrain inside!) If the gap (lash) is within spec, other things need to be checked. A valve could be sticking, causing the valve lash to expand. A
compression test would determine whether that is occurring, but those are hard to diagnose otherwise because of pressure from the springs. The best way is to remove the
head and disassemble the valve train, then check the valves for carbon buildup, both on the valve heads as well as on the shafts. Carbon buildup on the shaft can cause a valve to stick. Inspect the valve seats while in there for trueness; it is always a good idea to lap the valves. All the pieces from each cyilinder should be labeled and stored in their own cannister, to allow every part to return to where it was before teardown. This means each valve, spring, the little button, keepers for the spring and the disc that sits on top of the spring.
As the engine warms, the
parts expand from heat, so the noise from the valvetrain diminishes as a result, but that valvetrain sound shouldn't be that loud at startup.