In reaction, a bunch of icy asteroids shot into the inner solar system, pummeling early Earth and bringing it water, as shown in this animation. (sciencenews.org)
The Grand Tack nicely explains the formation of Mars, the layout of the asteroid belt and the delivery of water to Earth via icy asteroids. (sciencenews.org)
There may also be ways to sequester and protect some of a planet's water — probably delivered by icy asteroids (SN: 5/16/15, p. 18)-- during those first billion years. (sciencenews.org)