Can I connect a Homepod Mini to my Apple TV if I don't have any other Apple devices?

No, you need an iOS device to set it up. See HomePod mini - Technical Specifications - Apple (UK) > System Requirements:

• iPhone SE, iPhone 6s or later, or iPod touch (7th generation) with the latest version of iOS; or iPad Pro, iPad (5th generation) or later, iPad Air 2 or later, or iPad mini 4 or later with the latest version of iPadOS

tt2

You're welcome. 🙂

tt2