There is a parameter
initialseek
that allows players to be set to have the starting point at any number of seconds after the start.
Idea is to allow setting when the playback should stop as well or after which time the playback should not be possible.
Original request was asked for either time range support (initialseek as from and then time for how long to play back the video), or to have a "to" parameter that plays to that specific point in time and does not require initialseek.