nipok writes:
If the big bang was in fact caused by all matter we know of to have originally been contained in a single location and then it would have been stationary yes?
No. Particles appearing spontaneously in accordance with quantum mechanics have motions that cover a wide spectrum. There is no valid reason to assume a stationary start.
But the other problem with this concept is that the motion (or lack thereof) has to be in relation to something outside the universe (as you mention) and this puts it outside our purview. Our frame of reference is this universe, so relative to our frame of reference the universe is stationary and any relative motion to an external frame would be seen as the motion of the external frame -- the station coming to meet the train.
There is also the ekpyrosis theory of the universe starting with a collision between two 4D 'branes within a 5D (or greater) superuniverse, a collision that could have occurred over a wide area rather than a single point.
See
The Big Bang: What Really Happened at Our Universe's Birth? | Space
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