General synonyms:
* Found: This emphasizes the creation of something new.
* Create: Similar to "found", but with a broader meaning.
* Set up: This emphasizes the process of putting something in place.
* Start: This suggests the beginning of something.
* Initiate: This implies a formal beginning.
* Introduce: This suggests making something known.
* Bring about: This implies causing something to happen.
More specific synonyms:
* Prove: If you are talking about establishing a fact or truth.
* Determine: If you are talking about establishing a value or quantity.
* Confirm: If you are talking about establishing the validity of something.
* Secure: If you are talking about establishing a position or agreement.
* Insure: If you are talking about establishing security or certainty.
To give you the best synonym, please provide the context of the sentence you're trying to write.