Synonyms for "Push"
General:
* Propel
* Urge
* Thrust
* Shove
* Press
* Force
* Drive
* Impel
* Exert
* Promote
* Encourage
* Advocate
* Propose
* Recommend
* Advance
* Stimulate
* Boost
Informal:
* Prod
* Nudge
* Hustle
* Push through
* Get moving
* Get going
Specific to different contexts:
* Promote (product)
* Advocate (for a cause)
* Pressure (someone)
* Stimulate (economy)
* Boost (confidence)
Related to effort:
* Strive
* Endeavor
* Strain
* Exert oneself
The best synonym to use will depend on the specific context in which you are using the word "push."