Remember that all theories are best when they fit our observations, make predictions and hopefully can be tested. When we're discussing going all the way back to the origin of our observable universe, some version of the Big Bang is likely (Black Hole cosmology, hot big bang,  Penrose's Conformal cyclic cosmology and so on). Origin theories are made of complex math with many believing that the least complex should likely be closer to the origin then ones that have a lot of fine-tuning and extensive fudge math (making math fit what your bias, not what's probable/likely). Is it possible for RMOND/MOND variant theories to support a universe without a big bang variant, possibly, but it depends on what math you're using to account for things like dark energy, the CMB, and other cosmological phenomenon that needs to be explained.