> Sure they can. They can simply hire more women.
You're smart enough to know it's not that simple; even if one were willing to "just do it" it's not clear the unintended consequences would not result in a net-negative effect on women in engineering.
Fundamentally, if the source funnel is unbalanced, and you assume that there is a scalar "skill" quantity that is the economic factor of production employers actually desire, then it is mathematically impossible to hire-toward-parity without having a lower standard for hiring from the less-represented pool [0].
If you accept that ratio-correcting hiring mathematically necessitates lower standards for women then you need to answer some thorny economic questions.
Will the women whose skill is below the minimum skill of the men in your quota system be paid the same as the men (all of whom by mathematical necessity, will be more skilled)?. If they are paid the same as the men, it is a subsidy paid by the employer, the employer's customers, and the disemployed men who otherwise would have been hired but-for the quota. It's not clear to me that they bear any culpability for the social problem, or that the economic costs of this subsidy are sufficiently small not to have significant negative effects on those businesses. I know, I know: boo hoo, those poor businesses won't have two golden swimming pools of money, just one. But the reality is that the margins most businesses have between the cost of employment and the productivity of that employment is not, for most companies, rich Google-y numbers like 50%. If the margins are more like 10% it is entirely credible to me that such a subsidy will drive various arms of the business from ROI-positive to ROI-negative (or at least, ROI below just investing that cash in stocks). And then all those jobs we were planning to give to women will no longer exist.
If, on the other hand, the lower-skill women are paid sufficiently less than the men to balance the opportunity cost borne by the employer (for not being able to hire everyone above a minimum skill level) then the women need to be paid less than an open market wage (i.e. less than their skills would justify without a quota system, because the quota system is costing the employer lost productivity in men they would otherwise hire). So now the women are paying for the parity-seeking hiring. This will exacerbate the already high level of concern about fairness in compensation and will provide an additional disincentive for women to join this work force. Never mind that it seems perverse to have the women pay the employers for the privilege of working in a quota system.
Let me make a defensive statement lest it seem I am suggesting that women are less skilled than men: I am emphatically not. I'm saying that if you take the best five of 30 people and the best five of 100 people, the latter group will, with significant statistical regularity, be more skilled.
So what to do if ratio-correcting hire is DOA? It seems that there's an easier solution that has its roots in a long history of women conquering other obstacles; a generation of high-school aged women need to decide, en masse, that they will join engineering departments as a group and that they will stick to it with mutual support. This is direct action by the people whose well-being we are trying to improve, can be done without getting permission or cooperation from anyone outside that group, and solves the "boys' club" problem on day 1 of freshman year classes (because the club will be, by construction, full of women as well). I even have a slogan ready for them: "We're here, we're engineers, get used to it." I realize that coordinating this kind of movement is hard, but it is run-of-the-mill political and social organizing, and it seems to me like something that can actually work (as opposed to solutions that attack the symptoms of a skewed sourcing funnel).
[0] Proof sketch (hand-waving law-of-large numbers arguments, and assuming women's skills are distributed identically to men's):
1) If you reject quotas and hire simply for skill >= min_skill, then you will find more men meeting that criterion because there are men in the source funnel. So fixed-skill cutoffs are out.
2) If you have quotas (say 1 woman for every 1 man) then you can't hire everyone >= min_skill; you will instead hire the best among the people >= min_skill. The men will be pulled from a larger pool, and taking the best from a larger pool will result on average in a higher minimum skill level. So simply by taking the best N of the women and the best N of the men, the source funnel imbalance forces you to have lower standards for women