You deal with emergencies with international on call rotation?

"Follow the sun" rotations are a common way to handle 24h oncall rotations. Three regular shifts (8 hours of work plus some lunch break that gives you time for a short overlap at the beginning/end of the shift) during that region's local daytime hours, in three different regions with time zones roughly 8 hours apart.

That way nobody has to work nights and you still get 24/7 coverage.

I actually can’t think of a better way to do so.

Not just emergencies but good timezone coverage is nice for oncall, nobody likes getting woken up by a page at 3am.

But I meant things like having good and automated tests, deploys etc so everyone can be productive on their own without multiple people getting involved ("hey can you please deploy X for me when you are here?").