Could be worn spider gears in the differential. My 50 year experienced teacher in my driveline class told us that the gear will wear out which would explain the noise.

What happens in this case is the worn gears have extra space. When the transmission is moved to drive the driveshaft moves until pressure is on the gears. If the gears are damaged they will make noise when the car first starts to move (which is when the most pressure is applied to turn the wheels).

It may be this but is may be something else. A good sign is if the car clunks or lurch when trans is put in drive from park.