Actually, there are a few theories about how the language developed, but they all have one thing in common:
Language developed gradually.
Language developed in a society, along with our evolutionary changes, which were slow- they took hundreds of years to unfold.
As our brains became bigger and bigger, we wanted to communicate better with our kin (for example during hunting or to make ourpotential partners interested in us) and we developed symbolic thinking - the understandign that symbols stand for things. Those symbols were arbitrart sounds - which developed into words.
An example is the word "mama" which is similar in many langauges - we can imagine that this was a sound made by babies very early and that's how it became associated with words. Some sounds are similar to the things the discibe ("meow") but most are arbitrary