I'm frustrated over the same thing. Taps until I get some heat into the motor or the lifter pumps up, not sure which. I attribute it to what I have learned about the lack of availability of good hydraulic lifters. If they are aftermarket, it could very well be your problem. This is the reason I'm going to put a solid lifter cam and lifters back into my truck. At least they will all sound the same and not hear the same one or two clack away in the morning.

1953 Chevrolet 3100
261 cu inch, sm420, 3.55 rear, torque tube still,omaha orange, still 6 volt, RPO green glass, side carrier spare, all done
In the DITY Gallery
Video of the 261 running

1964 GMC 1000
305 Big Block V6, sm420, the next cab off restoration