General:
* Started
* Began
* Launched
* Commenced
* Opened
* Established
* Founded
* Introduced
* Set in motion
Formal:
* Inaugurated
* Embarked
* Undertaken
Informal:
* Kicked off
* Got going
* Got underway
Specific to groups:
* Inducted
* Welcomed
* Admitted
Specific to actions:
* Triggered
* Sparked
* Stimulated
The best synonym will depend on the specific meaning and context of the word "initiated" in your sentence.