/u/sowser wrote a great essay called Silence in the Sources: History at the Margins for the "Monday Methods" series.
/u/sunagainstgold has previously written about
/u/mimicofmodes has previously answered
(more below)
If you are interested in a methodological response, here is how scholars of antiquity learn about women in those societies.
In several Greek cities and in Rome, women are mentioned in law (such as marriage/divorce law) and in literature. Literary characters are constructions, true, but built on a socially common knowledge and perceptions. They communicate a lot. Authors particularly interested in women and their place in society are several: Euripides and poets of Roman elegy come to mind as ones who understood deeply the social irony of gender(ed) roles in their societies, but there are others.
And then, of course, there is archaeological and epigraphical evidence. From a variety of sites, we have evidence of material culture present in women’s daily lives, and attested in literature. From a site like Pompeii, we have a spectrum of lives frozen in a second, to include women in domestic contexts.
Perhaps the greatest sources are those of women speaking in their own voice, such as Sappho and Corinna. They are the exception, methodologically, but powerful voices.
While we do not have the volume of first-person accounts of women in classical antiquity, we do have a lot to work with. Scholars challenge each other to parse the evidence we have farther.
There are many outstanding scholars on the topic, but you couldn’t go wrong by beginning with the seminal work of Sarah Pomeroy and Mary Lefkowitz.