If the earth’s water had evaporated at that time, it would have been replaced by something else. It is likely to be recovered from ice-rich asteroids outside the solar system. Water was later discovered in asteroids and meteorites in the meteor belt, and this hypothesis proved very plausible. So is the claim that asteroids and meteors formed the Earth’s water? I can’t say that yet.
For this proposal to be true, the isotope ratio in the oceans must remain unchanged from four billion years ago. The findings show that the early hydrogen content of the Earth was much lower than that of deuterium today. This change in proportions causes early sunlight to heat both hydrogen and deuterium. There, hydrogen is lighter, so it could be thrown into space, leaving only deuterium.