How were galaxies and stars formed in the early universe?

When the universe began in the big bang, about 13.8 billion years ago,there was no carbon. It was so hot that all the matter would have been in the form of particles called protons and neutrons. There would initially have been equal protons and neutrons. However, as the Universe expanded, it cooled. About a minute after the big bang, the temperature would have fallen to about a billion degrees, which is about a hundred times more than the temperature in the sun. At this temperature, neutrons start to decay into more protons.

If this had been all that happened, all the matter in the universe would have ended up as the simplest element, hydrogen, whose nucleus consists of a single proton. however, some of the neutrons collided with protons and stuck together to form the next simplest element, helium, whose nucleus consists of two protons and two neutrons. But no heavier elements, like carbon and oxygen would have been formed in the early universe. It is difficult to imagine that one could build a living system out of just hydrogen and helium. The Early Universe was still far too hot for atoms to combine into molecules. 

The Universe continued to expand and cool. But some regions had slightly higher densities than others and the gravitational attraction of the extra matter in those regions slowed down their expansion, and eventually stopped it. These regions collapsed to form galaxies and stars, about 2 Billion years after the Big Bang.