Get an oil pressure gauge -- a proper one, not the dummy "gauge" on the cluster -- and check it while making this noise. If the oil pressure is okay you might have a timing chain tensioner issue. If the pressure is low you might have a pickup problem, a clearance issue in the engine (e.g. main or rod bearing with excessive clearance) or perhaps a problem in the oil pump itself (e.g. sticking bypass.)
Try to isolate the noise in the engine: front, rear? Top, bottom? Left, right?
When the noise stops, does it just sort of fade away or abruptly stop?
Once it's stopped, do you hear any other noises from the engine at any time (accel, coast, overrun, idle etc)?
When the engine was rebuilt, what components were used? Were forged pistons used? They can be noisy on cold-starts though this noise doesn't really sound like piston slap...
Has it always done this since you've had it or is it a new development?