Also, there is no way for vocabulary to exist on its own without grammar, as these are two sides of the phenomenon, we call language. Some signs of grammar had to emerge together with this, at once. However…
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Edit: Let's imagine a typical movie scene. Our nondescript individual points at himself and utters "Atuk" (yes, Ringo Starr!) and then points at his counterpart in this conversation, who utters "Carl Benjamin von Richterslohe". This involves quite an elaborate system of grammar, where we already know that we're asking for a designator, that this is not the designator for the act of pointing, and that by decidedly pointing at a specific object, we'd ask for a specific designator not a general one. Then, C.B. von Richterslohe, our fearless explorer, waves his hand over the backdrop of the jungle, asking for "blittiri" in an attempt to verify that this means "bird", for which Atuk readily points out a monkey. – While only nouns have been exchanged, there's a ton of grammar in this.
And we haven't even arrived at things like, "a monkey sitting at the foot of a tree". Which is mostly about the horizontal and vertical axes of grammar, along which we align things and where we can substitute one thing for another in a specific position, which ultimately provides them with meaning (by what combinations and substitutions are legitimate ones and which are not).
Now, in light of this, that specific compounds are changing their alleged "meaning" radically, when aligned (composed), doesn't allow for high hopes for this to be language.