This question was posed by an atheist on on Reddit some days ago, and I have been mulling over how I might answer it since. Instead of replying in that environment, I thought I might put my answer here.
Really, I have a number of points to make to answer that challenge.
1) He is much better at giving attention than I possibly can be. For me to give time and attention to one thing, I generally have to take time and attention away from another. God exists outside of time, so He doesn't face this difficulty. Imagine history is layed out like a book to you: You can spend all day reading and rereading one page, or skimming back and forth between chapters. That's what it's like to be outside the timescale experienced by the characters.
Furthermore, our issues of size are not an issue to God. He can look at galaxies in one moment of eternity, then look at atoms the next, and still have plenty of "timeless time" for each of us in between.
This isn't an argument that He does pay any attention to me. It's just an assertion that He can, at the same time, be God of All Creation and my Lord and Savior, without either taking away from the other.
2) God is a Creator, and creators tend to be mindful of their creations. I am also a creator, on a much smaller scale: I write software, I have built computers, and I dabble in creative arts. I have a family of creators: My wife is a performer, my mom is a painter, and my dad makes things with his hands. Every person feels a bit of connection to the things that they make with their mind, hands, and skills. Even the things that aren't necessarily of professional quality are special because they are ours, especially if we have put time and effort into them. We are God's creations, would He not be interested in us?
3) He said so. I take the Bible to be the Word of God, His self-introduction to humanity delivered through inspired human authors, including historians, poets, and prophets. In the Bible, we are described as His children by adoption. Jesus says that the smallest sparrow's fall doesn't escape His attention, and each of us is worth more than many sparrows. Jesus taught His followers to call the creator of the universe "Father". More than that, the Arameic word he used, "Abba", is a word that has strong connotations of affection and close relationship. God asked us to call Him "Dad". It would be utterly presumptuous of us to assume that relationship if He had not offered it first.
4) I believe because I have experienced. This is a point that can't really be debated, but I include it because it is part of my personal answer. I cannot prove it to anyone else, they can't disprove it to me. It would be like trying to prove the existence of snow-covered mountains to someone who has only ever lived in the desert: You either have to just take my word that I have experienced what I say I have experienced, or you can decide to disbelieve, but don't blame me if you aren't willing to come and see for yourself.
My life has always been better whenever I have involved God in it. The more I pray, and study His words, and seek to follow His ways, the more I understand that He really does love me. I have stumbled plenty of times, and gone off in my own direction; He's always ready when I come back to Him. That's not to say that my circumstances magically become easier when I'm following Him. But He settles my unsettled heart, gives me perspective on my problems, and helps me to make better decisions. He has even helped me out from time to time with downright uncanny coincidences.
I believe because I have seen. If anyone wants to come and see what I have seen, I would be glad to have you walk with me.