Is it possible to create an event on behalf of my own application? I tried using API Key but that doesn't work. I want all the event to be under my app's account. I don't want to make the user login. I just want to create new google Meet links.
No you must be authorized to write to a users calendar
if you check the documentation for events.insert you will notice a section called authorization
This section tells you what authorization scopes you need in order to be able to write to a users google calendar. A user must grant your application access to their data before your application will be able to write to it.
API keys are only used for accessing public data, for example the public google calendar holiday calendars you can read from them with an api key.
However to access private user data you need to be authorized.