I don't know what kind of events you have in mind that would trigger running a script but you can check out the tutorial how to run a function using pub/sub. It shows how to use scheduler based events but it's possible to use not-scheduled triggers;
Events are things that happen within your cloud environment that you might want to take action on. These might be changes to data in a database, files added to a storage system, or a new virtual machine instance being created. Currently, Cloud Functions supports events from the following providers:
HTTP
Cloud Storage
Cloud Pub/Sub
Cloud Firestore
Firebase (Realtime Database, Storage, Analytics, Auth)
Stackdriver Logging—forward log entries to a Pub/Sub topic by creating a sink. You can then trigger the function.
And here you can read on how to implement those triggers.
For example this documentation explains how to use storage based triggers in pub/sub.
If you provide more details of what exactly you want to achieve (what events have to trigger what) then I can point you to a more direct solution.