If it continues after the engine has been run a few times there are a couple of things that seem to help.
Prefill the oil filter before starting after an oil change. Change brands and/or weights of oil.
When I talked to Bill Cardell at Flyin Miata about this a few years ago his cure was to start them up and rev the piss out of them until the clatter went away. Not sure I agree with that cure.
The ticking doesn't damage anything, its just annoying and should go away once the engine is back in daily service.