Every experiment you can do to find out will tell you the same thing: "right here". If you measure how fast a galaxy is moving, you find that they all tend to move away from "here," and moreover they tend to move away from "here" faster the further they're away.

So did the big bang happen here and we're just spectacularly privileged to live in exactly that place? No. It doesn't matter where you perform the experiment, the answer is always "here". The explanation for this is that space itself is expanding. We're not seeing debris being thrown away from a central location where an explosion happened into some pre-existing space, what we're seeing is the metric expansion of space itself. All the distances between things are just increasing, not because the things are actually moving but rather because the space between them is literally growing. If you extrapolate time backwards far enough, all the distances become zero, and we call that singularity where our understanding of physics breaks down "big bang".

If you have two objects that are too far apart to affect each other, but that randomly happen to be stationary with respect to each other today, then tomorrow they will be further apart. There is no centre to this. The universe isn't expanding away from one spot, it's expanding everywhere like an infinite sponge soaking up water. And really, with the universe being infinite as far as we know, there can't really be another answer. It's not like the centre could have been "three quarters of an infinity" away from here.

> If you have two objects that are too far apart to affect each other, but that randomly happen to be stationary with respect to each other today, then tomorrow they will be further apart.

This statement is correct today, but only because of dark energy. You could have an expanding universe where it would be wrong (and for several billion years it was wrong in our universe), so it's not a direct consequence of expansion.

Your primary misunderstanding is that the Big Bang similar to an explosion originating from a single point.

The universe is likely infinite. The observable universe is a sphere with us in the middle. The edge of the sphere is where we see the oldest parts of the universe because the light from these distant places is just now reaching us, showing us what things looked like back then.

This sphere is getting bigger for an obvious reason, more and more light from distant places is reaching us. However, the sphere is also getting bigger because the entire universe (not just the observable universe sphere) is expanding.

Careful here not to imagine the entire universe’s expansion as a sphere, but rather every galaxy that isn’t locally bound to another galaxy by gravity is moving away from one another.

An oversimplified way to imagine this is to visualize an infinite 3D space with tennis balls each 10 meters from one another in every direction. Move forward through time and as the universe expands they are now 20 meters away from one another. Move back in time and they are 5 meters away from one another and so on.

There was a post a couple days ago where someone was staunchly asserting that space is not actually expanding and that objects really are moving away from one another kinetically, with multiple citations on the subject (which I didn't look too far into). There was a bit of discussion and a couple people agreed with them.

This was the first I'd heard about that. All modern material I've ever seen on astrophysics (the last twenty five years or so?) talks about the universe expanding.

How solid is the scientific consensus on this subject? Is it actually contentious at the moment, or was this person stating an belief that is currently kind of fringe?

Imagine you’re in a big ocean. You look out to your horizon. You realize that you’re in the center of the circle of that horizon.

Does that imply you are in the precise middle of the ocean? No.

You are always center of the horizon since you yourself made the horizon.

We are at the center of the universe we see.

Or.

The universe we live on is the surface of an inflating balloon. Where is the center of that universe on the surface of that balloon. It’s a meaningless/impossible question to answer other than saying the center is where you are or there is no center.

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So to answer OP's question, we don't know, right?

No, that's not right. We do know that no such "place" exists.

So the location of the big bang can't be plotted on a hypothetical xyz axis? Is that because our math is incapable of calculating this? Unknown variables?

The answer to "where did the Big Bang happen" is always "exactly where you are", no matter where you are. This is because it's not an event that happened in the universe, it is the universe.

Unfortunately I can't find the GIF with the expanding red dots that made it clearer, but the idea is that there is no preferred reference frame and thus no location that's "more important" than any other.

This image might help. Picture A is the location of galaxies at some given time, while Picture B is the location of galaxies at some future time. Pictures C and D show that the galaxies appear to be moving away from "here", wherever "here" might be, and the galaxies farther away from "here" appear to be moving faster.

https://allthatsinteresting.com/wordpress/wp-content/uploads/2013/03/big-bang-dots.jpg

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The reason why the center can't be plotted on and xyz axis it does not exist on the xyz axis.

In 2d think of the universe as the surface of a balloon being inflated there is no point on the surface of where expantion started (expantion started in the centre) as all points on the surface are moving away from all other points uniformly.

P.s. I know this I 3 days old