I disagree with both answers posted so far, they are too practical.
The question asked, whether Gaussian blur or average blur could ever be caused in-camera (as opposed to post-processing).
They can. Like the question suggested:
For example Gaussian Blur can be caused by camera jitters (fast micro vibrations)
Shake the camera either randomly with the following noise distribution, or shake it such that during exposure the camera is moved such that it is at a given position for a time proportional to the probability density function of the blur.
For the average blur, it should be a uniform distribution. For Gaussian blur, use a Normal distribution.
The average blur happens quite often, when an object is moving with a constant velocity during the exposure. (To be exact, with constant radial velocity around the nodal point of the camera, through a small angle.)
If you want to manually shake the camera to get any other blur, do it around the nodal point, and only through small angles.