My Homepod mini that I just bought is saying "there's a problem with the wi fi". The homepod screen will not appear on my iphone for me to get stated

Use the Home app:

If you don't see the setup screen*, you can manually set up HomePod mini or HomePod. Open the Home app, tap the Add button , then tap Add Accessory. Tap Don't Have a Code or Can't Scan at the bottom, then tap HomePod and follow the onscreen instructions.

from Set up and use HomePod mini and HomePod - Apple Support

Recommended settings for Wi-Fi routers and access points – Apple Support (AU)

Your Wi-Fi router needs to be set up with WPA/WPA2 wireless security and with any client/access point/wireless isolation/security feature turned off. These features prevent devices on your network from talking to each other, blocking traffic necessary when setting up HomePod.

tt2