Diagnosis
This is typically thermal expansion and contraction noises from the internal components as they heat up and cool down. It's more noticeable in very quiet rooms.
How to Fix It
First, confirm it's not audio interference. Temporarily disable "Hey Siri" in the Home app (Settings > Listen for "Hey Siri") to see if the clicks stop. If they do, it was the microphone array powering on to listen.
If That Didn't Work
Check for electrical interference. Plug the HomePod directly into a wall outlet, not a power strip, surge protector, or outlet shared with a fridge or other large appliance. Try a different outlet in another room as a test.
Heads Up
A single, loud pop when first powering on is normal. Continuous, rhythmic clicking or loud static is not. If the noise is loud, persistent, or occurs during audio playback, it could indicate a hardware fault requiring service.