How have you set this up, just by assigning the push button to throttle or by another means.
Does the throttle channel still show on the servo monitor, if it does it means that the ESC is not arming when you switch on, which is usually because it is not seeing a low throttle position, it's a safety feature that the ESC won't activate until the the throttle has been moved to the off position to prevent the motor from starting up when the transmitter is switch on with the throttle control in the wrong position.