When we open the lid of an unused cold bottle of coke the gas inside comes out fast with a sound. Why?

It is due to the pressure difference between inside the can and outside.

When you blow up a balloon you are pushing more air particles inside it than would like to be there. As soon as you pop it they all rush out. This is because they are getting pushed more from behind (from the many more air particles inside the balloon) than from the outside (the relatively few air molecules floating around in the atmosphere).

The exact same thing is happening with your coke drink. The drink is pressurised at the factory, meaning that there are more particles (not the same composition as air, but that isn't important) inside the can, per unit volume, than outside, so they rush out as soon as you open it.