Is there a truly stationary frame of reference? (part deux) I wonder if the belief that there is no truly stationary frame of reference is really true.  Here's my thinking, please poke holes in it and/or mock me :)
As we understand it, before the big bang the whole universe was a tiny dot, a singularity. At some cue or input or serendipity, that dot began expanding. When that singularity expanded to the size of a beach ball, or perhaps the earth, it should have had a center spot. Let's call that spot the Universe's Core. Couldn't we call that spot the One True Universal Frame of Reference? If not, why not? 
 A: 
Is there a truly stationary frame of reference? (part deux)

Yes. The CMBR reference frame. It's the reference frame of the universe. See this answer and note things like this: "There clearly is a frame where the CMB is at rest, and so this is, in some sense, the rest frame of the Universe".

As we understand it, before the big bang the whole universe was a tiny dot, a singularity. 

We don't actually know that. We're confident that the universe is expanding, and we extrapolate that back to an earlier smaller universe. But we can't extrapolate all the way back to a singularity with confidence. Have a read of Matt Strassler's article about that: 
"The notion that the Universe started with a Big Bang, and that this Big Bang started from a singularity — a point in space and/or a moment in time where the universe was infinitely hot and dense — is not that different, really, from assuming humans begin their lives as infinitely small eggs. It’s about over-extrapolating into the past".

At some cue or input or serendipity, that dot began expanding. When that singularity expanded to the size of a beach ball, or perhaps the earth, it should have had a center spot. 

You can find plenty of articles about this sort of thing, such as this one by Luke Mastin: "The linear dimensions of the early universe increases during this period of a tiny fraction of a second by a factor of at least 1026 to around 10 centimetres (about the size of a grapefruit)". 

Let's call that spot the Universe's Core. Couldn't we call that spot the One True Universal Frame of Reference? If not, why not?

If the universe was the size of a grapefruit, then the answer is yes. Some people will tell you the universe was always infinite, but we simply have no evidence of that. This assertion is something that has gained popularity since WMAP evidence suggested the universe is flat. See for example this article. But note that it's a non-sequitur. We simply don't know that the universe is infinite. And if it isn't, then we must allow for the universe actually having a centre. 
