ABSTRACT Lyman-alpha (Ly α) emission from galaxies is currently our most promising probe for constraining when and how reionization began, and thus when the first galaxies formed. At z > 7, the majority of galaxies detected with Ly α are in candidate overdensities. Here, we quantify the probability of these galaxies residing in large ionized bubbles. We create (1.6 Gpc)3 intergalactic medium (IGM) simulations: sufficient volume to robustly measure bubble size distributions around UV-bright galaxies and rare overdensities. We find ${M_{\small UV}}\lesssim -16$ galaxies and overdensities are ≳10–1000 × more likely to trace ionized bubbles compared to randomly selected positions. The brightest galaxies and strongest overdensities have bubble size distributions with highest characteristic size and least scatter. We compare two models: gradual reionization driven by numerous UV-faint galaxies versus rapid reionization by rarer brighter galaxies, producing larger bubbles at fixed neutral fraction. We demonstrate that recently observed z ∼ 7 overdensities are highly likely to trace large ionized bubbles, corroborated by their high Ly α detection rates. However, Ly α detections at z ≈ 8.7 in EGS and z = 10.6 in GN-z11 are unlikely to trace large bubbles in our fiducial model – 11 and 7 per cent probability of >1 proper Mpc bubbles, respectively. Ly α detections at such high redshifts could be explained by: a less neutral IGM than previously expected; larger ionized regions at fixed neutral fraction; or if intrinsic Ly α flux is unusually strong in these galaxies. We discuss how to test these scenarios with JWST and prospects for upcoming wide-area surveys to distinguish between reionization models.