> How did small atoms expand themselves to become size of galaxies.

They didn’t. Until roughly 380,000 years after the Big Bang, the entire universe was a thick opaque cloud of plasma of electrons and nuclei.

As the universe expanded, it cooled off enough to let the plasma become atoms, and the cosmos became transparent.

It is space itself that’s expanding, not the particles.

> I thought big bang was like a supernova where a massive amount of matter exploded.

This is a common misconception. A supernova is the explosion of a particular size star that occupies a point in space. The Big Bang was not an explosion, but the expansion of space.

Imagine infinite points packed together with infinite density. Those points occupy everywhere. There is no inside or outside.

Now imagine each of those infinite points moving further from its adjacent points, with the space between them expanding at an increasing rate.

For 380,000 years, the universe was entirely comprised of plasma but then it cooled enough that the electrons and nuclei combined to form atoms, molecules, dust, stars, planets and so on.

We have evidence of the above (post-380k years) since the discovery of the cosmic microwave background radiation (CMB).

>which external force was applied on universe to stretch it?

The best current hypothesis is Dark Energy, but we can only measure its effect. It falls outside the known laws of physics.

Edit: some relevant reading