In Toy Story 2, Woody is convinced to go to the Japanese toy museum, as he's worried about what will happen when Andy grows up.
However, from the same movie, two pieces of key timeline are established: we know that he is merchandise from a TV show that was cancelled in 1957 (from the Prospector), and that the movie is taking place after 1995 (from Tour Guide Barbie).
If Woody is a 40 year old toy, then you would expect that he would have belonged to someone before, and have already experienced being handed down. (Andy's mum does say he's "an old family toy", but she may just be saying that to get rid of Al) However he mentions none of this when Jessie and the Prospector tell their stories about what happened to them.
Is it ever established where Woody has been in the intervening time?