To achieve greater standardization among aircraft types, Boeing has recently published revised checklist procedures for the B747 Next Generation series aircraft in which the auto-throttle switch is armed as part of the after start procedure.
For years Boeing recommended that auto-throttle arming should not occur until the aircraft was approaching the departure runway (i.e., as part of the pre-takeoff checklist).
On the B737NG, with the auto-throttle switch armed, and the take-off go-around (TOGA) switches hidden from direct view under the thrust lever hand grips, it may be possible in a moment's lack of concentration to activate the TOGA button after engine start. Recall that engines are started at the gate, so the potential with wheel chocks removed and parking brake off (and TOGA inadvertently activated) is for the aircraft to move forward under full power.
As one pilot remarked, "I was a co-pilot where the captain hit TOGA just off stand - it was exciting for a few seconds. Push-back crew's eyes got quite large."
Boeing says, "We moved the arming of the auto-throttle point on the checklist to make all models common. They all only have FLAPS on the before takeoff [checklist] now."
Regarding TOGA, Boeing says, "It is possible to hit TOGA after engine start in all our models and have inadvertent acceleration, as TOGA switches are on the throttle quadrant of all our planes. The engines spool up slowly from dead idle and the crew is right there and start is generally during push-back or afterwards - it hasn't been raised as an issue in tens of millions of departures."