Better than "their own" -- develop free and open source software that will do it even in the participating countries. Which their people can trust because they can see and modify the code, rather than having to trust you, a foreign power.
That subverts the domestic propaganda machine there by allowing the people of the participating nations to talk directly to one another without being intermediated by a partisan spreading propaganda and imposing censorship.
There are a couple of issues with it though.
Let's think about Signal, Twitter, Facebook and Tor.
The US government is putting increasing pressure on social media companies like Twitter and Facebook to shape their content.
US government funded open source projects like Signal and Tor allow for the spread of US shaped social media in countries that want to limit it.
So the propaganda machine thrives , it's just that it's the US one.
(note I like and use Signal and Tor, an against censorship in China. This is just one aspect of a set of complex relationships. Etc etc)
This isn't going to happen, it's already happening and there are plenty of public examples of it.
Both 'sides' will (and really already are) marshal private sector tech, media and social media companies.
non-aligned countries would do best to develop their own tech and media infrastructure because they won't be able to trust anything else.
I think slide into a Cold War could be slowed down by people working in those companies having and enforcing ethical and professional standards. In a case like this one it would mean blocking any hacking attempts that you can, irrespective of where they come from.
For social media companies it would mean devising rules about what content you will and won't allow and enforcing those standards whether the posters are from Russia, Arizona or Afghanistan.