Agreed, the question of why Woody hadn’t been “outgrown” by a previous owner before now is a big one. (Add to that, the fact from TS2 that he didn’t know about “Woody’s Roundup,” or the existence of all these other Roundup-themed products.)
Here’s another issue I have - I can’t get the math to work out very logically for Woody to have originally belonged to either of Andy’s parents, unless Andy’s Dad was somewhat older than average for a first-time father.
Andy’s logical birth year options seem to me to range from 1988 to 1992 (If TS takes place in 1995 and Andy’s turning 7 = 1988; if TS3 takes place in 2010 and Andy’s soon turning 18 = 1992.)
Sputnik was launched in October, 1957, so Woody’s Roundup presumably ended in late '57/first half of '58. Woody is in such good shape for an old toy, his original owner must have been old enough to take decent care of him, so I’m guessing he/she was at least 6 or 7, which would put his/her latest possible birth year as 1952 (1958 minus 6). If 1952 is the latest birth year for the “parent,” and 1988 is the earliest birth year for Andy, the parent would be 36 when Andy was born - which, yeah, OK, his Dad could have been that age. (No way was Andy’s Mom that old, because that would put her in her 50s in TS3, and she doesn’t look that old.)
OK, here’s a silly “making stuff up out of nowhere” theory: First off, this is predicated on the idea that Stinky Pete had been removed from his box and put on display in the dime store (hence he was “alive”), then when they took down the “Woody’s Roundup” display, they packed him back in his box and put him on the shelf for sale, so he was conscious of being overlooked and left behind.
What if… Let’s say one of Andy’s grandparents bought one of the last Woody dolls as a birthday or Christmas gift for - not one of Andy’s parents, but an older sibling, or maybe even a nephew. Between buying Woody, and the gift occasion, the kid has dropped the Woody’s Roundup fad for the new Space fad, or whatever. Andy’s Grandparent decides to buy a different gift - spaceship or whatever - and puts the now-unwanted Woody doll - still in his Never Opened Box - in the attic (hey, maybe it will be worth something someday). YEARS LATER - Andy’s Grandparent dies. Andy is a little boy. Andy’s Mom/Dad are involved in cleaning out the Grandparent’s house, and they find the cowboy doll in his box in the attic. They give him to Andy, who is thrilled, takes him out of the box - and the rest is history! (When you have the “making stuff up out of nowhere” gene, there’s always a way to explain things. )