Re: After Big Bang where did the dust come from ? How the dust was formed?

Actually, at the Big Bang, not even gases were present. The Big Bang was 
not an explosion in the sense that you and I think of explosions - a fire
ball and lots of noise. The Big Bang was simply the coming into the 
existence of the Universe. The best account of what happened is probably
"The First Three Minutes" by Weinberg. I highly recommend it!

However, to answer your question, you are right. Astronomers often speak 
of interstellar dust. But where did it come from? To get to the answer, I
will need to run a very condensed timeline of the Universe. 

The Big Bang was a massive production of energy. Immediately after there
was an inflation period. Think of these two like blowing up a balloon. When 
you first blow on a balloon, while it fills with air, nothing much happens.
Then, the pressure will all of a sudden get large enough that the balloon
fills outwards rapidly. This was the "Big Bang" and the "Inflation" which 
filled out the Universe.

During the inflation period, the Universe cooled off enough to allow 
protons and electrons to get together to form atoms. Hydrogen was born.
For reasons that no one truly understands, matter attracts matter and this
hydrogen started to clump into lumps that condensed to form the first
generation of proto-galaxies and proto-stars and such (basically due to the 
gravitational attraction of the objects). This must have been 
a very "hot" time as the Universe would have still been seething with an
overabundance of energy. These stars burnt their fuel fast undergoing
nucleosynthesis in their cores. Then they died. In doing so, they formed
Supernovae and cast their core material into the surrounding space. Again,
gravity caused this material to clump into lumps.

More stars were born of the second generation, third generation, and so on.
Each generation burns up a bit more of the hydrogen fuel in the Universe 
and converts it to heavier elements (carbon, oxygen, silicon, and iron are 
some of the more abundant). Slowly, but steadily the non-hydrogen content 
of the Universe has grown. It is estimated that some 90% of the atoms in
the Universe are still hydrogen, 9% helium, and 1% everything else but that
1% has accumulated out of the repetitive life cycle of the stars.

And, of course, the explosion of stars produces a dusty cosmos which, as
Carl Sagan so aptly put it, means that you and I and everything around us 
is made of star dust! Hope this answers your question.