|MadSci Network: Physics|
There's another sort of frame transformation that doesn't keep the same t=0... it's what happens when you change all your clocks for daylight savings time!
Seriously, there's no such thing as an absolute t=0 (or x=0); you can always add an abritrary constant to all the times in a given frame and you'll get exactly the same physics. After all, time itself is always measured as a time difference between two events, not on some absolute scale.
The reason that the spacetime point t=0,x=0,y=0,z=0 remains the same under covariant transformations is simply one of convenience; some point has to remain the same, so it might as well be the origin of your coordinate system. You're perfectly able to change this origin before or after you transform into a different frame.
So the answer is no; the mathematics of frame transformation can say nothing about the origin of the universe. Einstein, after all, believed the universe had been around forever... until the experimental data showed otherwise. The moral: experiments can tell you about the universe, pure mathematics can't.
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