I doubt that. Children learn by observing. And there are still more women than men in nurturing positions.
1) obviously, the initial, first, nurturing position will be a woman (womb + immediately after. It can't even be a transgender). And we can change a lot with medicine, but we can't change this. We're not 1-2 years, or even 10-20 years away from changing it. It'll be centuries.
2) When we try to use law to fix this, the big example are the Nordic countries. They were among the first to loosen up professions and have very flexible laws. But the proportion of women in nurturing positions actually went up instead of down. Now this may be local cultural attitudes asserting themselves of course, but if this doesn't work ... what will?