Why won't my airpods pro connect to my iPhone 12 mini?

Ok. Your phone's Bluetooth is on as well? Both AirPods are in the case? Holding the open case next to your phone doesn't open the waiting dialog box? If all else fails, check this link: https://support.apple.com/en-us/HT207974

Are the AirPods in pairing mode (white led flashing on AirPods case)?

Then I would suggest to make an Appointment at the Apple store or reach out to Apple support to see if there is something wrong with the AirPods.