churches are better at incorporating women then the left is at this moment in time.

Church organizations tend to have more funding and larger congregations, they tend to have more veteran organizers and larger pools of people to draw on, and they tend to leverage a moral imperative that's been baked into the congregation's social life since birth rather than formulating a rallying cry lots of westerners haven't heard in decades.

I noticed this in a local dsa chapter where they had to meet a quota of 50 % women in org in positions of leadership, but they would quickly promote people who weren't ready for leadership as they had not enough experience

Young organizations are going to struggle with finding and promoting leaders. Lots of this is going to be trial-and-error. The fact that DSA leadership is making a good-faith effort to equitably include people is good. However, simply establishing arbitrary quotas doesn't work, because the people you're appointing as "leaders" don't have a following.

This isn't even strictly an experience problem. Large organizations are often amalgamations of smaller cliches and social groups. Extended families, religiously inclined business owners, and neighborhood/school groups will make up pockets of support in the church that the folks at the top of the hierarchy have to court in order to get anything done.

So perhaps the problem isn't that the DSA needs more women leaders (or... more non-binary males? Woof) but more outreach to women's groups that already exist in the area.

Are there local junior leagues, nurses unions, PTAs, or... idk... church groups, that DSA members could collaborate with? Rather than looking for women to be leaders, perhaps you can look for existing leaders in the community who are also women?