The Animus user who frames the historical stories in the first Assassin’s Creed is Desmond Miles.
Desmond is a modern-day descendant of several important Assassin ancestors. In the first game, Abstergo captures him and forces him to use the Animus, a machine that allows a person to experience genetic memories inherited from an ancestor.
The historical subject Desmond experiences first is Altaïr Ibn-La’Ahad during the Third Crusade. Desmond’s modern-day scenes provide the series’ framing narrative and establish that the historical missions are connected to a contemporary conflict.
William Miles is Desmond’s father and a senior Assassin, while Clay Kaczmarek is another Animus subject associated with Abstergo’s experiments. Daniel Cross is a later character linked to the Templar side, so none of them is the first game’s primary Animus user.