Direct Democracy can be introduced locally immediately in places where enough DD supporters will require that.

However, for some issues (environment, arms reduction) global coordination is needed.
For this, Simultaneous Policy Initiative may be useful.

The Simultaneous Policy Initiative is a peaceful political strategy to democratically drive all the world's nations to apply global solutions to global problems, including combatting global warming and environmental destruction, regulating economic globalization for the good of all, and delivering social justice, peace and security, and sustainable prosperity.
Can it work? Certainly worth a serious try.
Noam Chomsky