A synonym for “evoke change” that is closer in meaning to “support” could be “inspire transformation”.
“Inspire” implies giving someone the motivation or encouragement to do something. For example, “Her speech inspired the audience to take action.” When combined with “transformation”, it suggests that one is spurring on or instigating a significant change. This is similar to providing support in that it gives others the impetus to make a positive alteration.
Another option could be “encourage alteration”. “Encourage” means to give support or confidence to someone. For instance, “The teacher encouraged her students to think creatively.” Paired with “alteration”, it indicates that one is promoting or advocating for a change. This has an element of support in that it is nudging others towards making a modification.
“foster change” is also a good choice. “Foster” means to promote the growth or development of something. For example, “The organization aims to foster positive change in the community.” This implies a nurturing or supportive role in bringing about a change.