Why should God care?

Considering the vastness of the universe, why should God care about humans in general or me in particular?

First, I'd like to point out how there is a false assumption in this statement. You've equated size with importance and significance, which in reality have nothing to do with each other.

Is Jupiter, the biggest planet in our solar system more significant than Earth simply because it is larger? Considering how unique Earth seems to be, I'd say that it is not. Or, is a chunk of common rock sitting on the ocean floor more important than a human baby, just because it is bigger? Again, I'd say this is not true. Certainly, something can be both larger and more significant than another thing at the same time, but there is no direct connection between size and significance. Humans take up a very tiny amount of space in the vast reaches of the universe, but that does not necessarily mean that we are insignificant and unimportant. Size is irrelevant.

But that still doesn't answer the question of why we might assume God cares about humanity in general or individuals in particular. The short answer - He cares because He chooses to care.

But there's also a longer answer, and that answer to that lies in understand who God is - what His character is like. Let me give you some character traits of God and demonstrate how that's relevant to us. 

First, God is creative and all-powerful. Which means that isn't limited in creating this Universe in nice, simple, small areas. Science is amazing! The detail in a cell, the balance of an ecosystem, the majestic movement of objects in space and all expressions of amazing creativity. For the Christian, we can look at the universe around us and see God's fingerprints and be honestly awed. He's told us (through the Bible) that we can see the characteristics of God in the creation - and this is one of the reasons that the universe is so amazingly huge! If our little planet had been placed just about anywhere else in our galaxy, we wouldn't be able to see so much of the universe (either because of cosmic dust, which our galaxy is coated in, or through the crowding of nearby stars, etc. We're perfectly placed to be able to see beyond our solar system and just that fact alone is incredible). God can (and apparently did) choose to create a universe that expresses an unbelievable depth of capability for creating variety and opportunities - for exploration and discovery. This universe was made huge and detailed and discoverable for our benefit.

Next, God is all-knowing (or omniscient). Which means He knows everything about everything. He knows what every atom in the universe is doing at this moment and what it will do in every future moment. He has the capacity to pay full attention to everything at once. Which means He can know what's happening on Alpha Centuri or in the Horsehead Nebula or in your schoolroom and doing so is neither difficult nor dividing his attention. So He has the ability to pay attention to us humans individually and, if God wanted, He could have a million other things going on in other parts of the universe and it wouldn't make his attention towards us any less. So assuming that I have his undivided attention is simply an extension of understanding how powerful God actually is.

But that would simply imply that we're as interesting to God as, say, the moon. A unique chunk of rock, to be sure, but just another collection of atoms. However, God is more than just all-knowing and all-powerful. He is also loving. 

He is loving. He didn't have to create a universe that was filled with so much to explore and discover, but He did because He loves us and wanted to give us the best home imaginable. This point also circles around to the question of why God should care about us. He cares because one of the characteristics of God is love. He created us because He wished to love us and be loved in return. That was the whole purpose of making humanity.  You want to know why you are here? Why you are alive? That's the answer.Because God chose to love you and wants to be loved in return.

So the answer to the question of why we should assume God would care about me or anyone else is because it is both God's nature and His choice to do so. To think otherwise would diminish who He is. To reverse that idea, if we assume that the universe is too huge for God to notice us, then that is saying that we don't think He is actually all-knowing. To think that the universe is too complex to be divinely created (which seems a bit backwards, but some people think that way), is to think that God is less than all-powerful. To think He'd create a thinking, feeling, relational people (humanity) and then not care about us implies that He is not loving - and if God does not love us, then honestly, all Christianity is empty and your life is completely pointless. We can explore that idea a bit more, if you'd like, but it kind of wanders off topic, so I'll end here.

Did that seem to answer your question, or do you still feel a bit unsatisfied with this idea?