Watch the vary first scene and pause the shot when the computer type comes up. The date is 2/19/98 and the call is being traced. Later after Neo is freed, he is told the year is thought to be 1999. ( Some time could have passed, but...) At the end of those first scenes the agents know about Neo and are about to waste no time finding him. We are lead to believe he is freed just days after, rather than months.