How do I accomplish the initial install? It looks like I need. an iPhone or an iPad.

Correct, from HomePod mini - Technical Specifications - Apple:

System Requirements

• HomePod mini with the latest version of software
• iPhone SE, iPhone 6s or later, or iPod touch (7th generation) with the latest iOS; or iPad Pro, iPad (5th generation or later), iPad Air 2 or later, or iPad mini 4 or later with the latest iPadOS
• 802.11n Wi-Fi internet access

tt2

Set up and use HomePod - Apple Support