General:
* Begin
* Commence
* Initiate
* Launch
* Inaugurate
* Embark
* Undertake
* Set about
* Get going
* Kick off
Informal:
* Get started
* Jump in
* Hit the ground running
* Get cracking
* Dive in
More specific:
* For a journey: Depart, set out, take off
* For a project: Launch, implement, roll out
* For a meeting: Convene, assemble
* For a performance: Open, premiere, debut
The best synonym will depend on the specific situation and the desired tone.