Is the problem the time it takes to unlock the phone and find the icon, or the time it takes the app to start up?
If the first, some phones allow you to put a camera shortcut on the lock screen (my old phone did, my current one does not). If yours doesn't you could see whether any third party lockscreen replacement app will allow it (it's 5 years or more since I used one, so I don't know much about the current state of these). Or add the camera to your quick settings: if your system doesn't allow that there are apps like "Shortcutter" which do, and looking at my phone it looks like Open Camera (below) also provides that option.
If it's the time the app takes to load you could try an alternative camera app and see whether that loads faster. Open Camera opens slightly faster than the Pixel camera on my phone (though the Pixel camera also opens quickly). If not then I'm afraid all that's left is buying a faster phone.