Adding tasks to someone else's OAuth 2.0 calendar?

Question

Google

Hello. There is an internal portal. The portal has a calendar (for each employee) with tasks. The goal is to synchronize this calendar with mobile devices (android, iphone).
For synchronization, as I understand it, Google Calendar is quite suitable for me.
You just need to get into the employee's g-calendar and send him events from the portal.
I started to deal with authorization, registered here cloud.google.com/console#/project/ , created a project. even managed to connect to it from java code (using json file).
And then I suddenly discovered that this is not a fig, not the calendars of employees, as I understand it, I connected to my calendar.
It turns out that each employee will have to register on this page (this is very difficult) and throw me json files. This option is very complicated, is there any way to simplify it?