Why my iPhone 16 Pro Max's activation date shows April 1978?

Open Settings > General > About > Model - does it begin with a 5? If it does, the phone is refurbished not by Apple. As such refurbished phones not by Apple will usually display the date you're seeing and has no warranty from Apple. If you thought you were buying a brand new phone, that's not what you got. I'd see what the return policy is from the seller, but don't expect any assistance from Apple with this.

Marinero_Master wrote:

Model begins MYW*****, serial number begins JK2*******

That's interesting and does not indicate the device was refurbished. I would contact Apple Support directly for help. You can tap the Support Button at the bottom of this page. If you're in the US, you can call Apple at: 800-MY-APPLE. You can visit an Apple Store Genius Bar for in-person help. You can tap this link --> Contact - Official Apple Support

Is that the same number stamped on the SIM tray?

You have is refurbished iPhone and it does not have a warranty unless one was provided by the merchant that sold you the iPhone. Apple is not warranting the item.

There is no time restraint for refurbished products appearing for sale. It may or may not have been refurbished by Apple.