We are composed of matter and we are conscious, we take this as being axiomatic. Given we have one certain example, the question is then how does the body do it, and how could we do it in other substrates: how do we go from "just physics" to mind [1].
The short answer is: chemical reactions start a chain reaction of abstraction towards higher and higher forms of collective intelligence.
For some reason, perhaps something with the way the Hilbert space vector obeying the Schrödinger equation which we usually call "the universe" is [2], but also given the ridiculous breadth and depth of possible explorations of the biological pathways [3], "chunks" of matter tend to group together, they group and form stars and planets, but they also group and form formaldehydes and acetaldehydes and many more. Given enough tries, across multiple environments, in some lucky hydrothermal vents abiogenesis was probably started [4]. Once we had the first agential "chunk" of matter, a group of matter which has a definition of the boundary between a "self", no matter how tiny [5], and an exterior environment, it was more of a game of waiting (~4 billion years) for this tiny agent to grow into an agent with higher-order thinking, self-referentiality, metacognition, and the likes.
Neural networks, as in matrix multiplications, are not conscious because they have no mechanism for deciding what is the environment and what is their own, they are a hammer, sitting there, expecting to be used, not a lacrymaria olor [6], exploring the environment for survival and fun. Could we have neural networks in an agent-like architecture starting to behave more like thermostats, setting goals for themselves? Probably.
[1] "From physics to mind - Prof. Michael Levin", https://youtu.be/_QICRPFWDpg?t=85
[2] "Sean Carroll: Extracting the universe from the wave function", https://www.youtube.com/watch?v=HOssfva2IBo
[3] "Nick Lane, 'Transformer : The Deep Chemistry of Life and Death'", https://youtu.be/bEFzUx_j7tA?t=279
[4] https://en.wikipedia.org/wiki/Hydrothermal_vent
[5] https://en.wikipedia.org/wiki/Physarum_polycephalum
[6] https://www.youtube.com/watch?v=sq6Y54mxjOg