I can’t help directly, but I’ve been interacting with a lot of people trying to leave, so I’m aware of a bunch of resources that exist. You’ve probably seen many or all of these, and they’re not AI-specific, but maybe it will still help.
The most important thing I can say is, get out fast. Don’t count on whatever works to get out now to still work in a month. The borders aren’t closed yet, but they might be soon, especially for military age men. (I think the chance of this has gone down some, but it remains a live possibility.) If it’s at all possible for you financially, get out first and figure out what to do long-term after that.
With that said, here’s my list:
Эмиграция из России в свободный Мир - advice about what countries have what visa restrictions, how to cross the border, how to find jobs, lists of jobs and grants and such
Reboot Start-up Nation—Israeli-based support and job seeking network
Creatives at Risk—another post-your-resume-and-view-job-openings location
Help with work—list of jobs and resources
https://www.helpwithjobfinding.org/ - fill out a form to hear about job openings
Zimin Foundation—help for people in academia under threat because of their opposition to the war
IT Evacuation / DigitalXy—Telegram channel, what it says on the tin
IT вакансии в Армении - Telegram channel about IT jobs in Armenia specifically
Good luck!!!
Oof, this is both terrifying and inspiring.