Alongside Neo

What with all the craziness of The Matrix conceptually (not to mention all the philosophy and theology thrown in the mix) the narrative structure itself is necessarily simple. Just imagine if Neo's journey out of the Matrix was a series of flashbacks that occur as he's on his way to save Morpheus. Not only does that sound way more confusing, but it also ruins the big reveal: that the world we think is real, our world, is a virtual reality.

Because this reveal is the huge point of the film, the narrative takes place alongside Neo's discovery. When Neo is shocked, we are shocked. Our emotional journey mirrors Neo's disbelief. Morpheus tells Neo that he has:

MORPHEUS: ...the look of a man who accepts what he sees because he is expecting to wake up.