Earliest departure, as a time of day in the origin airport's local time — HHMM, e.g. "1600".
Deliberately not RFC3339 like departure_time: this is a wall clock with no date, and a
value that cannot be read as HHMM is rejected rather than ignored, so a dropped time window
can never be mistaken for a filtered result.
Optional: when set, the search starts the day's schedule at this time and returns flights
from there onwards, so send it only when a specific time window was requested — the day's
earlier flights are then no longer returned. The time of day carried by departure_time is
NOT used for this: that field selects the day to search.