What you need to do is get the water simulation to start later in time. My animation in this example is 150 frames long at 25 frames per second. That's 6 seconds in total. So, to get the simulation to start later in time, I entered the following details in the fluid simulator.

Start time of 1 (1 second into the simulation) allows the fluid to 'settle' for 1 second. End time of 7 making a total of 6 seconds of fluid simulation. Which is correct for the 150 frames.
I must admit, when I tried this the fluid wasn't in sync with the moving obstacle but that just involved changing the keyframes for the obstacle in the IPO editor.
Hope this helps