You can set up a HomePod Mini by holding your iPhone close to it or start the setup process manually from the Home app.
How to Set Up a HomePod Mini
Best Apple HomePod and HomePod mini tips and tricks
Set up voice recognition on HomePod or HomePod mini - Apple Support
How to Set Up HomePod mini or HomePod (2022)
Single HomePod mini setup. Surprisingly room filling for its minuscule size. : r/HomePod
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How to set up home theater audio with HomePod or HomePod mini and Apple TV 4K
Here's my current HomePod mini + Apple TV 4K setup. It's not as clean as some others, but it works : r/HomePod