The Wachowskis embedded so many layers of symbolism into their cult film trilogy, people are still uncovering secrets in the Matrix movies decades later. The first installment - released in 1999 - is particularly rife with Easter eggs; visual, verbal, and audible clues all hint at themes and key plot points from the second and third films in the trilogy.
These secrets are buried with mixed degrees of subtlety. Christian allegories are laid thick, from biblical-inspired names like Trinity, the Nebuchadnezzar ship, and the human city of Zion, to Neo basically becoming Jesus in a trench coat (his journey of death, rebirth, and acquiring miraculous powers parallels the son of God's). If that isn't enough Matrix fan theory fodder, Neo's status as "the One" is also hinted at from the very start, since his name is an anagram of the word.
While you might have picked up on some of the more obvious homages (like when Trinity tells Neo to "follow the white rabbit,") there's lots of other foreshadowing you probably missed in The Matrix.