To address the first part of your question – The Big Bang (which happened 13.8 billion years ago) created ~only hydrogen and helium. So, no water existed in the early Universe (a) because there were no oxygen atoms formed in the Big Bang and (b) the early Universe was too hot to form water molecules even if oxygen was present.
>>> during Earth's creation?
Whether water was present on the Earth from "day one" of its formation (~5 billion years ago, much later than the Big Bang) is still an open question, but part of why it might be unlikely is that the Earth is close enough to the Sun that it was too hot for water to stay as ice or liquid on Earth's surface (before Earth's atmosphere formed). Water that forms in comets (further away from the Sun) doesn't have that problem, as comets would be in colder parts of the early Solar System.