How do I verify the authenticity of my iPhone 12 Pro Max?

Buying only from Apple or an authorized reseller. Anything else can be counterfeit.

Look for a Google Play Store app, and look for the Apple App Store app. Finding the former is bad, and finding the latter is expected.

Some other suggestions: https://convergeddevices.net/how-to-spot-a-fake-iphone/

Serial numbers are routinely copied from legitimate devices, and cannot be used to identify counterfeit devices.

Though an IMEI check won’t tell you if the device is a counterfeit, I’d also avoid using any online IMEI checks, other than the CTIA-provided tool: https://stolenphonechecker.org/spc/consumer

Devices sold in China, Hong Kong, and Macau supported 2 physical Nano-SIM cards.

The iPhone 12 Pro Max was discontinued in September of 2021.

If you already purchased and have doubts, return it and get your money back.