We develop a new method to determine the distance between a high-redshift galaxy and a foreground screen of atomic hydrogen. In a partially neutral universe, and assuming spherical symmetry, this equates to the radius of an ionized bubble (R B) surrounding the galaxy. The method requires an observed Lya equivalent width, its velocity offset from systemic, and an input Lya profile for which we adopt scaled versions of the profiles observed in low-z galaxies. We demonstrate the technique in a sample of 23 galaxies at z > 6, including 8 at z = 7.2-10.6 recently observed with JWST. Our model estimates the emergent Lya properties and the foreground distance to the absorbing intergalactic medium. We find that galaxies at z > 7.5 occupy smaller bubbles (& SIM;0.5-1 pMpc) than those at lower z. With a relationship that is secure at 99% confidence, we empirically demonstrate the growth of ionized regions during the reionization epoch for the first time. We independently estimate the upper limit on the Stromgren radii (R S), and derive the escape fraction of ionizing photons ( fescLyC ) from the ratio of R B/R S, deriving a median value of 5%, which, on average, represents the lower end of the photon budget necessary for reionization.