I know the earliest they
can appear is the sixth game or so, because it will start mentioning hitting streaks of that length (Matt will talk about it too). Their batting average will be highlighted and it will say they have a 6-game hitting streak.
I just want to make sure you know I'm not talking about those league leader boxes that show up during cutscenes - I've never seen one of those in season play either. What I'm talking about is during the batter walkup, where their season stats show. Most of the time it'll be hitting streaks, noting a guy in the top 10 in a particular stat...stuff like that. It's not like there's going to be something for every player. It's nowhere near as diverse as those quick game ones - those were specially made for each player just for exhibition games.
This fix is more about getting the bad info (the quick game stats) out of the picture than anything else.