If God were like us -- limited, and able to concentrate on only a few things at a time -- then you might be right; He probably wouldn't care about us. After all, you and I can barely keep track of what's happening in our own lives, let alone what's happening to everyone else.
But God isn't like this! We are limited -- but He is not. We can't keep track of everything that's happening -- but He can. You say God is "too big" to care about us, but that's the point: He is so great that He knows about even the smallest details of our lives. The Bible says, "Nothing in all creation is hidden from God's sight. Everything is uncovered and laid bare before the eyes of him to whom we must give account" (Hebrews 4:13).
This is why you can trust Him and turn to Him with every concern you have. We are not alone, nor are we left to make our own way blindly through life (although many people still do). God made us and He loves us and cares about every detail of our lives -- and the proof is that He sent His Son, Jesus, into the world to offer us eternal life.
Perhaps you like to think God doesn't care about us, because it leaves you free to live any way you want to. But that's a dead-end road. Instead, face honestly your need of God, and turn to Christ in faith and trust.