Camera object is visible during the game scenario

that is because you are too close to the action.

the camera is too “large” and it cuts off when is too close up to an object and this gives the impression of a hole in the image.

you could fix this by changing the Near Clip Plane

Edit → Project Settings → General Settings, there is a Near Clip Plane

but another alternative is to move the camera game object back and then use the lens options to change the zoom. like those 35mm 75mm that stuff

but if is a 2D game better to use an orthographic camera which doesn’t has this near clip issue