The BB says that the initial energy would have congealed into individual particles - protons, aka Hydrogen ions (later to become Hydrogen atoms). As the universe cooled, some of these would have collided together, sometimes sticking together to form Helium and Deuterium (and some Lithium). For various reasons, nothing heavier would have been formed , which was a BIG problem for the BB until Hoyle (who, coincidentally, always hated the BB) figured out that heavier stuff would have been formed inside stars. Stars also generate negligible amounts of Helium (compared to expected BB quantities), and would consume any deuterium.

So, basically all the Hydrogen, Helium and Deuterium we can see would have come from the BB. But - and this is the thing - we also know from experiments here on Earth how likely Hydrogen is likely to fuse into Helium/Deuterium. Applying that to expected conditions post BB means we can calculate how much Helium and Deuterium would have been formed from the primordial Hydrogen.

This was first calculated by Gamow, who came up with (IIRC) 75% Hydrogen, 20% Helium, and 5% Deuterium. This was from first principles, before observations were possible.


Take a look at the Hubble Ultra Deep Field, and this article. Younger galaxies have a number of features, like they're much smaller, more irregularly shaped, etc. From the HubbleSite:

Back to work - I'll get to the rest later