This is the Cosmological Argument. I've answered it most thoroughly here, but also to some extent here, here and in a comment here. Jake and Carl Sagan have their own answers here. Look through them and choose your own solutions from that lot to either accept or argue.
I'll just add that simply because the Big Bang seems to imply something which seems nonsensical to you doesn't necessarily mean that it is actually nonsensical, let alone impossible, or that it even implies what you think it does.
- SmartLX