Thanks to everyone that has replied to my thread.
I've had ABS systems in my cars for many years (albeit I've never had a Toyota before), and I've never heard a sound like this. For what it's worth, the bang does not
occur when starting then driving forward. It only occurs after backing up (which in my case also involves turning the steering wheel to the driver's side) then driving forward.
The bang happened several times today while I was out. I tried to listen more closely to it to isolate it's position. It seems that the bang is more on the driver's side than between the driver and passenger seats, and maybe located higher up than under the car, say in the engine compartment in front of the driver.
I had a brilliant idea that the bang could be caused by the A/C system coming on, so I shut it off before parking. Unfortunately, my "brilliant" idea didn't have a speck of light in it; the bang occurred with the A/C off.
The other thing I noticed is that it's not a metallic bang or a clunk. It's a muffled bang like a plastic door opening or closing. The bang is also not time sensitive, i.e. if I put it into drive after backing up and just sit there for a few seconds, no bang occurs. If I then go slowly forward, the bang only happens after the shift into 2nd, no matter how long that takes.
Thanks again for all the ideas. I'd love to believe it's the ABS system, but the bang doesn't sound like a "click" or "motor sound" as the manual describes.
ps - I did try backing up, then putting it into park, then drive, and started going forward; the bang still happened. Darn, I thought I could fool it by putting it into park first