Short answer: the association between the grammatical genders and sociological genders happened very early in Indo-European, but it was an association rather than an equivalence and had many exceptions.
I read that greek/latin used words that translate to "kind" to describe the noun classes (as we use "gender" today), so maybe the speakers of those languages didn't have the association that one noun class was masculine and one was feminine?
That is indeed the origin of the word "gender" in the linguistic sense; it's cognate with "genre" and "genus".
However, from a very early point (thousands of years ago at the latest), two of the Indo-European genders were strongly associated with sociological gender in humans. In Latin, Ancient Greek, and Sanskrit, for example, names and words for individual people are almost always masculine or feminine based on the person's sociological gender.
(Exactly how early is still debated, because the oldest attested I-E languages, the Anatolian branch, only shows a two-way distinction between animate and inanimate. Some linguists believe Proto-Indo-European originally had this two-way distinction, and developed the masculine-feminine-neuter split later, after the Anatolian languages split off; other linguists believe Proto-Indo-European originally had the three-way distinction, and the masculine and feminine merged in Anatolian.)
It should still be noted, though, that this was more of an association than a strict rule. Grammatical gender was fundamentally a property of the word, rather than the person (or thing) it referred to, which could lead to "mismatches" that sound weird to English-speakers. In Ancient Greek, for example, diminutives tend to be neuter, so words like "child" (paidíon) were neuter regardless of whether the child was male or female (compare modern German Mädchen "girl", which is neuter for the same reason). And words that could refer to people of any sociological gender still often had a fixed grammatical gender: in Latin, "human" (homo) is always grammatically masculine, and "person" (persona) is always grammatically feminine.