Best Firms for Breaking into Gov/Nonprofit Leadership?

Hey all, just curious if anyone is aware of what firms provide the best exits to places like the UN, State Dept, Fed Reserve, Treasury, WEF, World Bank, etc.?

My current firm (incoming CA at ACN) seems to take on quite a few projects in this area, and I was told getting the best decision-making or advisory roles in the gov/nonprofit sectors comes from being able to build a very strong network of career-advocates while also having the work experience/education to back that.

I just left the new hire celebration day at ACN in DC, and during that time they mentioned being #1 in DC for nonprofit work while also getting to do some really cool technology projects with the government. Their commercial work is only 20% of the population out there, which is why I chose this office.

I just like to make sure I leave no stone unturned, as plan to attend GW's GSPM program or GU's MSFS program to begin making this move. I want my working years to count while I'm doing that, however, so I just want to make sure I'm not missing anything in terms of what other firms might give an even better chance at getting my feet wet working with NGOs, nonprofits, and the government overall.

I know this ask is fairly nuanced, but any input here is welcome!