I'm surprised that scientists believe water was delivered. Why wouldn't water be one of the by products of the big-bang and during Earth's creation?
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.
http://en.wikipedia.org/wiki/Supernova_nucleosynthesis.
Nucleosynthesis says that at the end of the life of a star, heavier elemnts are formed as a byproduct.
http://en.wikipedia.org/wiki/Graphical_timeline_of_the_unive...
If you're interested in cosmology, there are a ton of fascinating popular science books on the topic, and research is very active and ongoing. As an introduction, I recommend Cosmos by Carl Sagan. It's a bit outdated these days, but the main points hold and it's a fascinating read from start to finish. Alternatively, if you prefer video, check out Cosmos: A Spacetime Odyssey with Neil deGrasse Tyson. It's an up-to-date retelling of Sagan's original idea.
There weren't any Oxygen atoms around until long after the big bang, and only a handful (in cosmic terms) of non-Hydrogen atoms.[1]
H2O molecules couldn't form until Oxygen had been synthesized, which occurs when a star exhausts its Hydrogen and begins fusing its Helium[2]. So water probably didn't exist until well into the the first or second generation of stars.
> One of the leading hypotheses on Earth’s formation is that it was so hot when it formed 4.6 billion years ago that any original water content should have boiled off. But, today, two thirds of the surface is covered in water, so where did it come from?
Temperature is just an expression of mean kinetic energy of particles. If gases (especially light gases) are hot enough, their kinetic energy can correspond to a velocity that actually exceeds the escape velocity of Earth's gravitational well. This is how hot gases can be removed completely from the Earth's atmosphere (and then solar wind & radiation take care of removing it from there). Even at today's atmospheric temperatures, helium gas (molecular weight of 4 atomic mass units, much lighter than molecular oxygen, nitrogen, etc.) can escape from Earth's atmosphere.
(EDIT: actually, on second thought, N2 would have a higher molar weight than H2O...)
As far as methane, it seems to all mostly be biogenic[1].
[1] - http://www.astrobio.net/news-exclusive/methane-on-earth/
Isn't it possible that early Earth contained many times as much H2O as it does now (like some of those Jovian satellites that are covered in hundreds of miles of ice), and what we have now is simply what's left after the majority "boiled off"? That way, there would be no need for comets and asteroids to return the lost water to Earth.
Other comments in this thread mention vast amounts of water trapped deep inside the Earth, as well as outgassing of nitrogen after the Earth has cooled down. Perhaps the water near the surface of the early Earth did "boil off" entirely, but what we have now is the result of subsequent outgassing?
DNA has a 'half-life' of ~500 years. Panspermania may still be a viable theory, but it is very restricted in terms of stellar distance/time in transit.
http://en.wikipedia.org/wiki/Standard_conditions_for_tempera...