Individual words, yes.
But the concept of speech was predetermined by factors already present. With any language, they all have the same principles and do the same thing. communicate ones thoughts.
Languages were also invented. But communication, both auditory and visual, existed long before humans: most other species communicate in similar way. Humans used verbal and non-verbal signals for a long time before realized the significance of what they were doing. The reason human languages are so similar is the same reason sparrow languages are so similar: all the common traits of members of the same species - sound-producing apparatus, brain structure, life needs, social unit organization. Not to mention the overlap, interaction and mixing of populations from at least 30,000 BC to the present; thus the learning of one another's languages, other alphabets and numerical notations.
The concept, function and principles of communication were neither invented nor discovered: they simply evolved, like flowers and wings. All humans did was organize sounds into spoken languages and marks into symbolic languages.
It wasn't until much later that some humans began to study these phenomena which already existed.