QUESTION: Is there any theory that claims that space appeared before time or vise versa? Or did they appear together. I.e. are they inextricably connected?
ANSWER: That's kind of an oxymoron, don't you think? Before time? I mean, if "before" is defined in terms of a location in time, how can you have something "before time?" That makes no sense at all, and I'm aware of no mainstream theory that purports space existing independently of time.
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QUESTION: Thank you, though I find your answer unsatisfactory. I am certainly not a physicist, but neither am I a child.
While semantically you are correct that this is an oxymoron, this is simplistic and may not apply to the laws of physics and they were initially. You are referring to a simple future past timeline.
While you claim that there are no theories that separate the two, it is interesting to look at Professor Gunter Nimtz who claims that zero time can exist ( whether you agree or not)
' these experiments create a timeless zone: a space without time. Entering the zone, the wave functions of photons freeze..'
Cramer (1988) has proposed that every entity in the universe (every particle) sends out waves both forwards and backwards in time. Observed events occur when a forward wave collides with an appropriate backward wave.
Finally, when one moves beyond fundamental physics to the domain of cosmology -- the question of the birth of the universe -- things become even slipperier. For a while cosmologists thought about the Big Bang as the moment at which time began. There was no time, and then -- BANG! -- time came into existence. But now a subtly different interpretation has emerged (Hawking, 1993; Smith, 1997). Perhaps there was no time, not only at the moment of the Big Bang, but in the very early universe, for a "little while" after the Big Bang (it is not clear what a "while" means in this context!). Perhaps time came to emerge only gradually, as the universe got larger and larger, and cooler and cooler. After all, at the microscopic level, time still doesn't exist! An elementary particle today is still "at one" with the particles that existed at the very beginning of the universe, bound together by quantum nonlocality.
The four first dimensions are usually depicted as three spatial dimensions followed by a fourth time. While these are obviously folded into each other, the sequence as an analogy is still interesting.
I'm not implying that you're a child, just simplifying things. I said that there were no mainstream theories that purported timeless existence of three dimensions. In that I mean accepted by most theorists and supported by experimental evidence. I'll stand by that. If such a theory becomes picked up by people who spend their days pondering such questions then I'll examine the math and reconsider. The superluminal tunneling you point out has been largely measured to be a spurious non-effect. The other paper is from over 20 years ago and has gained no traction that I can see. Basically, there's still no mainstream theory that posits space existing independently of time. If you're unsatisfied with that, then I'm sure time (ironically) will bear out any theories that will be more satisfying to you.