The ignition switch has 2 separate contacts. One for gauges, lights, radios and the other for the starter relay and the ECU via the neutral safety switch located at side of the AT unit. Your problem may be caused by one of these below.
The second contact of the ignition switch,
The neutral safety switch
The starter relay
The starter itself including the solenoid
One of fuses between these including cables.
Since you need to attempt at least two times, I think it may be caused by the ignition switch or the neutral safety switch. In case of the neutral safety switch, shifting AT lever several times pushing the release button before the try (engine start) would be a way to find the cause.