We present two models for the COVID-19 pandemic predicting the impact of universal face mask wearing upon the spread of the SARS-CoV-2 virus--one employing a stochastic dynamic network based compartmental SEIR (susceptible-exposed-infectious-recovered) approach, and the other employing individual ABM (agent-based modelling) Monte Carlo simulation--indicating (1) significant impact under (near) universal masking when at least 80% of a population is wearing masks, versus minimal impact when only 50% or less of the population is wearing masks, and (2) significant impact when universal masking is adopted early, by Day 50 of a regional outbreak, versus minimal impact when universal masking is adopted late. These effects hold even at the lower filtering rates of homemade masks. To validate these theoretical models, we compare their predictions against a new empirical data set we have collected that includes whether regions have universal masking cultures or policies, their daily case growth rates, and their percentage reduction from peak daily case growth rates. Results show a near perfect correlation between early universal masking and successful suppression of daily case growth rates and/or reduction from peak daily case growth rates, as predicted by our theoretical simulations. Our theoretical and empirical results argue for urgent implementation of universal masking. As governments plan how to exit societal lockdowns, it is emerging as a key NPI; a "mouth-and-nose lockdown" is far more sustainable than a "full body lockdown", on economic, social, and mental health axes. An interactive visualization of the ABM simulation is at http://dek.ai/masks4all. We recommend immediate mask wearing recommendations, official guidelines for correct use, and awareness campaigns to shift masking mindsets away from pure self-protection, towards aspirational goals of responsibly protecting one's community.