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Primordial neutral atomic gas, mostly composed of hydrogen, is the raw material for star formation in galaxies. However, there are few direct constraints on the amount of neutral atomic hydrogen (H i) in galaxies at early cosmic times. We analyzed James Webb Space Telescope (JWST) near-infrared spectroscopy of distant galaxies, at redshifts ≳8. From a sample of 12 galaxies, we identified three that show strong damped Lyman-α absorption due to H i in their local surroundings. The galaxies are located at spectroscopic redshifts of 8.8, 10.2, and 11.4, corresponding to 400 to 600 million years after the Big Bang. They have H i column densities ≳10 22 cm -2 , which is an order of magnitude higher than expected for a fully neutral intergalactic medium, and constitute a gas-rich population of young star-forming galaxies.