It seems that we do in any case. You can set limits on the density of baryonic matter (i.e. normal matter, made of protons and neutrons) by looking at the relative abundances of the lightest nuclei (hydrogen, deuterium, helium and lithium). If there are too many baryons (protons and neutrons) around, it becomes impossible to construct a model of Big Bang nucleosynthesis that can be reconciled with the abundances we observe.
(The proposed alternate theory revises Newtonian dynamics so that less force is needed to produce very small accelerations.)
I wouldn't call MOND a theory. It's more of an empirical fit.