The isotropic 2.7 deg. K Cosmic Microwave Backround radiation is consistent with a Universe that is expanding...
The recession of distant galaxies (again, isotropic), is consistent with an expanding Universe.
"sides" of the universe have nothing to do with it.
how do we know it isnt just some phenomonom that causes movements around us?
Because if it were a localized motion effect, it wouldn't be isotropic; we would appear to be moving away from some distant celestial objects, but towards others.
or... that this system is contracting?
Because we don't see any evidence for an isotropic blue shift.
saying it has no sides down plays the big bang theory
BB Cosmology says nothing about the Universe having "sides" (boundaries). An unbounded Universe is entirely consistent with BB Cosmology.