Yes, you can put it in D just as soon as you let off the key and the engine is started. Gentle on the accelerator until you start moving, though.
If you've got a back road and some time, you can put a manual button on the starter solenoid and that will allow you to crank in any gear, so that you can see how your vehicle would react to being started in D or R or any other setting. It *shouldn't* damage the transmission, but it will work the starter a little harder. It may save you a gram or two of fuel on restarts while you're waiting for the transmission to engage back to D, etc.
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