It could be the water pump. Depending on the production date, your Avalon might have the old design pump or the new design. I have no way to tell which pump is which, and am only relaying what I read on the Intarwebs. My 2009 Avalon was built in September 2009. The transition date for the new pump design was around February 2009. Again, I am only relaying what I have read, and nothing has been verified by someone with authority to verify it.
If the oil changes were extended, the VVT components will develop a sludge and start wearing. Over time this wear accelerates, as the space increases, thereby making the wear worse with each hit. You need to get a trained ear on the noise. If you know which end of the wrench to hold, you could remove the drive belt and see if the noise changes. If it does, then take a close look at the water pump under the pulley. If you see pink crusties, then the pump is leaking and needs to be replaced. The best way to see this area is to remove the right front wheel and look up at the bottom of the water pump.
If you decide to remove the belt, make a clear drawing of the belt routing.