I'm not expert on the data and I'm for sure not saying there isn't any sexism. But the wage gap has been answered by many people looking at stats and doing proper comparisons putting years worked, hours worked, and experience in the field into context. Check out Thomas Sowell's writings on these topics. The TLDR is that in many of the stats used to say their is a wage gap they don't account for factors other than sex. When you account for those in many companies women actually are paid slightly more than men.

When you think about greed and free markets this isn't even a problem that would need to be solved. As a sexist business owner you'd be forced to choose your bigotry over profit. If you had employers that just refused to pay women as much for the same quality work based solely on sex it would create a situation where a new employer could enter the market and capitalize on this stupid business decision and hire the women at a discount and put the competitors out of business or force them to change their practices. Things like this are often just tools used by weak men to gain power over the people. To give the state more power because it is the only institution that can save us. Its a fallacy. Sexism is a moral problem and the state can't fix that. They can only make it worse. When I look at society today it is like there are forces hell bent on pitting people against each other. Many of these forces hide fairness or equality but the outcome is division and bitterness. Its very sad.