Diagnosis
This is almost always a Bluetooth or Wi-Fi issue on your iPhone, not the HomePod. The setup handshake uses Bluetooth.
How to Fix It
On your iPhone, go to Settings > Bluetooth and ensure Bluetooth is ON. Then, force quit the Home app and reopen it. Bring the iPhone very close to the HomePod (within a few inches). Unplug the HomePod for 10 seconds and plug it back in, then try immediately.
If That Didn't Work
Restart your iPhone. Then, on your iPhone, go to Settings > General > Transfer or Reset iPhone > Reset > Reset Network Settings. This clears Wi-Fi and Bluetooth caches. You'll have to re-join your Wi-Fi network, then try setup again.
Heads Up
Both devices must be on the same Apple ID and your iPhone must have a working internet connection (cellular or Wi-Fi) during setup. Also, ensure your iPhone is running a compatible, recent version of iOS.