Game window size vs scene window size

As my first scene, I want to have a menu that is not displayed in fullscreen mode, but when you click the “start game” button, the window should be switched to fullscreen with a resolution of (for example) 19201080.
What I have done is setting the first scene to “Activate fullscreen: no” plus "Change window size: 640
360". However, in the settings for the game, I have selected 19201080.
In the scene that should start when clicking “start game”, I choose “Activate fullscreen: yes” and "Change window size: 1920

As a result, this will give me a resolution of 1920*1080 (as this is the settings for the game) for the first scene, which basically makes every object in the scene much smaller than they really are.

Did any of this make any sense? Any way to make this work other than to make my object three times larger (so they will be scaled down to normal size)?

There is an option to choose, when changing the game resolution, if you want to “Use this size as default size for new scene cameras ?”
If you choose yes, the new camera will use this new size as their default size. That is too say, when you change the scene ( So as to let the camera be (re)created ) the area displayed by a camera will be larger if you choose a large resolution.
On the contrary, if you chhose no, the new camera will stay with their initial default size which is the size of the original game’s window : The game will be distorted to fill the new window size.