Short answer
Your eSIM usually starts working after you arrive in the supported destination and it connects to a local network.
Before your trip
It may show Activating or No Service. This does not always mean there is a problem.
After arrival
Make sure:
the eSIM line is ON;
the eSIM is selected for Mobile Data;
Data Roaming is ON for the eSIM;
you are in the country or region covered by your plan.
Good to know
In most cases, data validity starts on first connection in the destination unless the app says otherwise.