Although Intelligent Reflective Surfaces (IRSs) are a cost-effective technology promising high spectral efficiency in future wireless networks, obtaining optimal IRS beamformers is a challenging problem with several practical limitations. Assuming fully-passive, sensing- free IRS operation, we introduce a new data-driven Zeroth-order Stochastic Gradient Ascent (ZoSGA) algorithm for sumrate optimization in an IRS-aided downlink setting. ZoSGA does not require access to channel model or network structure information, and enables learning of optimal long-term IRS beamformers jointly with standard short-term precoding, based only on conventional effective channel state information. Supported by state-of-the-art (SOTA) convergence analysis, detailed simulations confirm that ZoSGA exhibits SOTA empirical behavior as well, consistently outperforming standard fully model-based baselines, in a variety of scenarios.