Why is Apple Intelligence not showing up on my iPhone 15 Pro Max?

Also, check your iPhone model number. Does it end in CH/A? If it does, it was manufactured for China and Apple Intelligence won't work on the phone until it is approved in China, regardless of where the phone is used.

Are you actually in the US?

Have you updated to the current version of ios? The current version is 18.1

If your iPhone model number ends in CH, then you have an iPhone manufactured for China and you cannot have Apple Intelligence until it is approved for Chinese model iPhones.