General:
* Appear
* Surface
* Come out
* Rise
* Show up
* Materialize
* Develop
* Come into view
* Become apparent
More specific:
* Erupt (for a sudden and forceful emergence)
* Break out (for a sudden and unexpected emergence)
* Issue (for something coming from a source)
* Emanate (for something originating from a source)
* Extricate (for emerging from a difficult situation)
* Resurface (for reappearing after being hidden)
Figurative:
* Flourish (for something becoming successful)
* Progress (for something developing positively)
* Gain prominence (for something becoming more important)
The best synonym depends on the specific context of your sentence.