Using all of modern science and technology, scientists still can't explain why you feel like you exist.
In neuroscience, this is called the "binding problem." "Binding" refers to your brain taking all of the different perceptions, thoughts, and actions that are happening simultaneously, and melding them together to create a single entity that is you. The "problem" is no one being able to explain how this happens. There are a few theories; for instance, there's a type of electrical wave (the gamma wave) that sweeps through your brain about 40 times a second under certain conditions, and which some scientists believe could be the answer to the binding problem.
Maybe there's another possibility. Maybe the reason we can't figure out what makes you into one entity is because you aren't just one entity.
Think about it. How often do different parts of you want different things? You want to eat a cupcake, but you want to eat healthier. You want to sleep in, but you want to do a 6am yoga class. Don't you feel like there might be more than one of you at these times? And have you ever asked yourself a question, and gotten an answer – or several different answers? It's like there are several people inside you, talking to each other.
A rare type of surgery has occasionally been done for severe epilepsy, in which the two hemispheres (halves) of the brain are disconnected from each other. What results from this is essentially two people living in one skull. They can respond independently, although only one of them (usually the left side) can use language to do that. But the other side (usually the right side) can communicate with images. Whatever the right side does, the left side makes up a reason why it did that. Because it can't stand the thought that there are parts of itself that it isn't in control of. (And don't we all sometimes do things without really knowing why?)
Maybe we're all two people living in one head. They just communicate with each other very effectively, and one of them maintains the delusion that it's the only one. In fact, if there are two, couldn't there be more? Could there be tens of consciousnesses that are all part of you? Hundreds? If there are even two, then is there a you that exists at all?
Ask yourselves what you think of this.