This is a deep and excellent question. Science has no unambiguous answer to what "aware" really means. For example, a flower turns to follow the sun as it crosses the sky, so in some sense it is "aware," but that is not really what you mean. We can program a computer to respond correctly to queries about its existance and performance, but I don't know anyone who accepts this as "aware" yet. While many are working on this, and there are some working definitions and theories, sentience, or self awareness, and consciousness are still mysteries

We might have a problem with the definition of "scientific viewpoint". I'm going to risk the can of worms here. There is science, an unbiased search for knowledge or truth no matter where it leads; and there's science, a search for completely naturalistic/materialistic explanations for everything without ever making reference to anything metaphysical. The first answer is according to the second definition. I'm going to suggest that my first definition is actually the better definition, even though it's not currently the favored one. And by that definition, as eveidenced by the first answer, this is one of the points where science can suggest the existence of God (and I won't quibble here over the nature of that God--it's not the place). Physics indicates that self awareness is not a property of matter. Thus, if one will have it, physics points outside itself for that property. It's not that this is an unscientific or illogical proposition, it is that the spiritual implications are unacceptable to many people. That is my "purely scientific viewpoint".

Not a lot of answers from the "pure" scientist, so how about some slightly im-pure science..... As we grow, in our brains we create an abstract model of the "world for us". The "awareness" portion of our brain looks at that model and says "Oh, I'm directly aware of Reality". This is an error. In truth we are just a mental construct simply aware of it's own database. The "advanced" nature of human brains over other ones, means ours is more likely to build a mental model that matches Reality in a more effective way to manipulate that Reality. But it can never match Reality directly....the unalterable speed of light ensures that. There are a lot of interesting directions to go from here, but not in context to the question. In terms of the question, the problem is the question itself. Matter does not in fact become aware of it's own existence. What we as humans are "aware" of is just a wetware simulation that lags significantly behind the truth of existence by the limits of the speed of light...both outside our brains and inside.

I'll give this a shot. I think this is more of a philosophical question than a physical one. Matter becomes aware of its own existence when it realizes that someday it will cease to exist and tries to find ways to continue its existence. This logic seems to make sense because if it doesn't continue its existence then it would be pretty hard for us to observe such a specimen. If it is alive then it must have some means to continue to survive previously and we can only guess that it must be aware of its own existence to survive.

I suppose there can be no horribly strict answer to this question... however, I shall try to put this as simply as possible. The brain is, essentially, a massive set of circuits. If you are at all familiar with computers, the brain works as the motherboard, similiar in structure to something like a CPU or chipset. Like the motherboard and CPU in a computer, the brain collects data from various forms of input (eyes, skin, mouth, etc.) and bases conclusions off of this data. When you're feeling sick, that's the response of nerves in your stomach sending unusual or negative data to your brain, and your brain concluding that something is amiss. This is much like how a motherboard collects data from thermal sensors placed throughout it, and deciding to inform you of this or shut down if it begins to overheat. Thus, in a way, people are no more aware of themselves than computers are. The main difference, of course, is that people use more complex systems, and include what is essentially extraneous data (emotions) into the equation. This may be a slight dreary outlook on human life, but from a purely scientific viewpoint it's essentially true.