Many surviving sources concerning 'philosopher women' in this period are not very flattering. For example, in Aristophanes' comedy 'Assembly Women' (391 BCE), the women of Athens take over the ekklesia, the space in which Athenians citizens (males only) gathered to cast their votes, and state debating frivolous rubbish, such as curses against slaves who grass up their female masters' adulterous intrigues.

This does not guarantee that inhabitants of 'ancient Greece' uniformly thought women were really stupid; as a contrary example, in the surviving scripts of Plato's 'Republic' (c. 390 BCE), women in the 'kallipolis' are described by (the now long-deceased) Socrates as having equal right to being 'guardians' and eligible for philosophical and academic training as males.

Employing sources like these two, Republic especially, is pretty difficult and a tricky exercise in judgement but I hope it's helpful.

I would say it would be simply unthinkable. There are a couple of references in Plato (I'm thinking of Phaedo and Symposium specifically) where one of the characters basically says "right, let's get the women out of here and do some philosophy".

There may be references to the possibility of women taking part in philosophy, but it is not likely that these were anything other than satirical.