Background of the issue:
I created a new product and added a new container with the Avada theme. After saving it as a global container, I did the translations for other languages.
Symptoms:
The global container does not appear in ATE mode. I need to go to the Avada library, container, and do it manually.
Questions:
Is this an issue that the global container does not appear in ATE mode?
While you wait for my colleague to take over the ticket, let me try to help you with the issue quickly.
When you are translating page, you are only translating content built inside that page, not loaded from Global template etc. You can translate them as you said or send those elements for automatic translation also from WPML > Translation Management.