could you describe it in a bit more detail? Does the noise happen when the engine is cranking? Or is it a noise that's after the engine is fired up and the starter motor winding down? And for how long does it do it?
Your 'elephant' description matches closest to the starter motor being dirty and makes a noise after the engine has started. It would last for about 2 seconds or so and is a wind down kind of sound. It is nothing to worry too much, very common on many cars not just the A2. I have had it for a number of years and ambient temperature can affect the severity of the sound. If this is not what you're describing, I'm sure other members can help if you give more details.