Formal:
* Made friends with
* Formed a friendship with
* Cultivated a friendship with
* Established a bond with
* Gained the friendship of
Informal:
* Palled up with
* Got close to
* Hit it off with
* Made buddies with
* Became friends with
More nuanced:
* Took under one's wing (implies mentorship)
* Supported (implies providing aid or encouragement)
* Connected with (implies a shared interest or understanding)
The best synonym will depend on the specific situation and the tone you want to convey.