This is the problem, not (only) men's attitudes. The most screwed up part is that this inequality often holds even in female dominated professions, like librarians and teachers. I'm into forcing companies to do things rather than waiting for the attitudes of millions to change, esp. when the effect of that attitude only increases the income and options of the people whose attitudes you are trying to change.

Institute quotas and penalize companies if they don't make them. In the beginning, companies may have to hire women that are less talented than the men that are available to them, but if the positions are there, women in general will up their games to compete with each other for them. It's basic economics.