Assuming you're using some version of iOS 11?
If you have raise to wake enabled you can simply raise your iPhone then swipe right on the lock screen.
If you don't have raise to wake enabled or any for any other reason this might be faster - press the power button and immediately swipe right on the lock screen.
The newer iPhones in particular load the camera very quickly so by the time you finish the right swipe the camera is auto-focused and ready to go.
Another tip would be to make sure you have the camera icon docked on your home screen. This would allow you to access it quickly if you're in an app. You could try using control centre too, but you would have to swipe up from the bottom twice in most apps.
Currently there are no hardware shortcuts like this on iOS.