Correct it does exist, but we can of course set a limit...question is where? The reason in theory the function goes on forever both ways is because the function does not know where you are.
Maybe you are a billion years from the start, so it will continue backwards negative for a while, but of course, you be talking about the past as present, which makes it go forward.
I state this in response to your comment about a sin value existing before the one infront of it.
We need more information to see where we could possibly put a limit on (like x>0).
I know astronomers and physicists have been researching things like star formations/life times, light...and physicists using calculations to determine other material, but outside of religion, I wonder if they can come up with something pretty concrete.
Ex: you say this happened billions of years ago, but we might have gone too far on our 'sine' function.
example: -2pie is farther back than -pie, but both yield the same value. This would all change if we used a graph more like e^x (
sorry if I am getting off topic/not making sense, just let me know)