I can offer another way to understand the movie.

The book that Neo opens in the beginning is a book called Simulacra and Simulacrum written by Jean Baudrillard. Neo pulls a computer chip from the book. This is a signal to the audience that we can understand and interpret the computer simulation through the lens of Simulacra and Simulation.

In short, like very short, Simulacra and Simulation explains how a "system of control" is created and sustained. Baudrillard was not referring to a computer simulation but rather, symbols and signs. Language is one example of this. The Matrix, then, can be understood as our culture, an interconnected set, or matrix, of symbols, signs, and ideologies that inform the behavior of those who identify with it. For The Wachowski Brothers, this matrix, our Western, capitalist culture, is a system of control meant to be dismantled. All of these symbols, signs, and whatever else, are designed to control our minds and render us passive consumers rather than creators of Reality.

Baudrillard understood culture - the world of media, technology, advertising, and marketing - and the language and other symbols meant to represent "things" as separate, but still indistinguishable from, true reality [which we can never know].

Because of that, we're already living in a simulation.