Hum,
it is perhaps better just to say that there was no momentum given to objects during the big bang implosion, and that the total momentum is zero.

The galaxies we see are not moving through space, they are moving with space.
It is space that is expanding (ie, think cherries in a cake as it is baked )

BTW, the spirals we see are due to shock/density waves `rotating` and don't reflect the true motion of the stars.

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`Irony` actually does mean `metal like`...