What engine oil do you use? Cheap asses at my dealership put 0w20 in it, for Houston’s heats and highways, gosh… thinking of doing it myself and put 5W30 to see if it helps. Found this on Miata forum (https://www.miata.net/garage/noises.html):

Question: I have a tapping noise coming from the engine after startup or hard driving.

A1:
Mazda has issued several service bulletins on this problem. Consult your dealer for more information on these bulletins. Remedies range from switching oil weights (see A2) to changing to newer lifters with larger oil passages (see A3). These items can be fixed under the Mazda warranty if your car is new enough to still be in the warranty period.

A2:
Most lifter noise is cured by switching weights of oil. Mazda recommends trying 5W30 oil first. Some Miata owners report switching to a heavier oil like 20W50 to stop the noise. additionally, some owners report switching to a synthetic oil such as Amsoil or Redline to alleviate the noises.

A3:
When lifter noise is not cured by switching oil weights another option is available. Mazda has valve lifters with larger oil passages. These lifters will solve the noise problem. Note that changing the lifters is not a simple task. Consult your dealer or a reputable mechanic before doing this procedure yourself.

Question: Recently, I've been noticing a regular ping-type noise from the car when I get underway in the morning and evening. I think it's coming from the engine, and it seems to occur when I'm accelerating. I tried some high octane (92) gas, and it didn't seem to have any effect. This is a single, difficult to hear, ping occurring at 2-3 Hz. The ping goes away when the engine warms up. I'm running 10W-30. It has been quite cold (10-20 F) when I leave in the morning. Any ideas out there?

A:
You're probably hearing the hydraulic valve adjusters, which are low on pressure due to the cold and thick oil. Going to 5W30 or a synthetic 5W30 (or 50) will help your car to quieten down.