UPDATE: TinyCo has verified that Frame of Mind Part 5 is when this will trigger.
Hey there Tribblemakers!
Sorry for the delay on this one, been curled up in a corner on meds trying to make it until my flight out in a few hours.
Once you go aboard the Enterprise (as this wouldn’t trigger for me in Quahog), you will be prompted by Peter for a mini quest titled “Away We Go”. THIS IS A TIMED QUEST! (I am still verifying if there is a trigger. I had just passed Frame of Mind Part 6 & 7 in my game.)