We present new constraints on the cosmic cold molecular gas evolution out to redshift 6 based on systematic mining of the public ALMA archive in the COSMOS field (A3 COSMOS). Our A3 COSMOS dataset contains ∼ 700 galaxies (0.3 ≲ z ≲ 6) with high-confidence ALMA detection and multi-wavelength SEDs. Combining with ∼ 1,200 CO-observed galaxies at 0 ≲ z ≲ 4 (75% at z < 0.1) in the literature, we parameterize galaxies’ molecular gas depletion time and gas fraction each as a function of stellar mass, offset from the star-forming main-sequence and cosmic age. We propose a new functional form which provides a better fit and implies a “downsizing” effect and “mass-quenching”. By adopting galaxy stellar mass functions and applying our gas fraction function, we obtain a cosmic cold molecular gas density evolution in agreement with recent CO blind field surveys as well as semi-analytic modeling. These together provide us a coherent picture of galaxy cold molecular gas, SFR and stellar mass evolution.