Your lake analogy doesn’t work, because in the case of the Big Bang there was no “lake” to drop the rock in.
It’s more like you dropped the rock and a tiny, tiny lake appeared exactly where you dropped it and started growing. Where in the lake did you drop the rock? Everywhere, because the whole lake was all exactly where you dropped it. And there wasn’t even a lake until you dropped it.
Only it’s still wrong, because a lake has an edge, and the universe doesn’t. So the nearest analogy we can get would be to make the expanding lake the surface of a sphere, like a soap bubble, that starts incredibly small, exactly where you dropped the rock (whatever that means now), and expands bigger and bigger. Again – where in the surface of the bubble did you drop the rock? Everywhere, because, again, the whole surface was all exactly in the place where you dropped it. The bubble wasn’t even there before that. There’s no special “centre” anywhere in the surface bubble.
And that’s STILL not good enough, because the spherical bubble is a two-dimensional surface embedded in three dimensional space, and it has an inside and an outside. Whereas the universe is three dimensions of space and one of time, and it’s not necessarily embedded in anything else – it just “IS” .
And frankly, if your mind didn’t give up at that point, I’m amazed, because mine certainly does; you just have to accept the basic ideas and fall back on the mathematics to work out what that means for a 4 dimensional universe. But the question and answer are still the same: where in the universe did ~~you drop the rock~~ the Big Bang happen? Everywhere. The whole of the universe was all packed up together incredibly small, not “in” anything else – and it all grew. There’s no special centre of the universe. And – as far as we currently know – there wasn’t even a universe “before” that. “Before” in quotes, because even time only started at the Big Bang.
No, my mind won’t do that either. The “no space or time before the Big Bang” picture is only one of several. The problem is that the maths that describes the universe basically breaks down at the Big Bang. That may or may not always be the case; the jury is still out. For now, it’s the best description we have.
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