I’m warning you: these will be stupid.
Over the last four years in MLB (2005-2008), the first hitter of the season for each team is hitting .306/.375/.454 (120 plate appearances)
Teams who get the first batter of the season on base (46 of 120) average 79.5 wins.
Teams whose first batter records an out (74 of 120) average 81.9 wins.
Denard Span led off the Twins 2009 season with a walk. Teams that do that (12 of 120) average 80.7 wins. 4 of the 12 made the postseason.
Teams starting the season with a triple have not made the postseason in this time frame. (the only example – 2006 Cubs – 66-96)
Every team whose first batter reaches on an error has made the postseason in this time frame (the only example – 2006 Dodgers – 88-74, NL West Champs)
7 of 29 teams whose season started with a strikeout made the postseason (which is pretty close to the percentage of teams overall – 7 of 32 = 21.9% while 29 of 120 = 24.2%)
The first hitter of the season for each team that eventually makes the postseason is hitting .286/.375/.464 (which mirrors almost exactly the overall numbers above)
In conclusion, none of this tells us anything, you just wasted all the time it took you to read this.