Before the car turned on to Elm -- the windshield -- bullet resistant glass -- and other 'targets' in the way.
If he had done it when the car was directly below, (fishbowl) he would have had to lean out the window making him a visible target and in a very awkward position.
From his little snipers nest built of boxes of books he had a perfect stand to rest his weapon on and make totally unobstructed shots after the car past.
Go stand in that window some time and you will realize how damn easy those shots were.
The view from the TSBD looking at Dealey Plaza as the motorcade approaches:
You can pan around the sniper's nest to see stacks of textbooks:
From the scope, you can see that the target is limited from this angle, and there is the bulletproof glass. Also, the car moves quite a lot as it comes toward you, making it difficult to track the shot:
As the car makes the left turn, it is even more difficult to track as it is now a left-right motion:
Once the car emerges from behind the tree, JFK's entire back is available. You can aim the rifle just above where you are shooting, and the target enters the scope. It is almost impossible to miss from here:
After the shooting is over, it tallies your score, and replays your shots, Zapruder style:
If you hit JFK right after the car passes the tree, the "Zapruder" relay will show him reacting just as he passes the sign as he does in the real film. You also have the option to play the replay from different angles. I realize this is only a simulation, but it does give an idea of what Oswald saw (and I reduced these screenshots to preserve bandwith). Also, you may not make the same shots as Oswald. You may succeed with one shot.