I don't think that
has ever been a problem in Star Trek.
After all, for this to be a problem, the enemy would have to be proactive. But Star Trek is about the heroes being the active party. It is them who choose when to engage in an adventure, and this timepoint of their choosing resets the clock for the teaser of each episode. The ship enters the orbit of the target planet with Alpha Shift in charge; the ship responds to the emergency call by summoning Alpha to the bridge and then
the teaser begins.
On the other hand, when an episode begins without Alpha in charge, nothing much is happening. "We are en route to a conference" is a classic way to launch a teaser, too.