perhaps they put in the general term "the people" because the knew those who constitute "the people" might change as time went on.
Who told you that?
It's only a living document in the sense that it contains provisions for it's own modification. Those provisions require a vote in the state legislatures, and generally a proposal by Congress, alhough a convention can also propose amendments, but the "convention" method has never been used, except to create the Constitution in the first place.