It is create with using on the specific Contact id. May i know can i create an engagement with specific user contact number that save in my contact list instead of using the contactids and what is the keyword i should using in the associations .
It is currently not possible to create an engagement by specific a contact number instead of contact ID.
You can however, use the CRM API | Search to search for contact that equal to the particular phone number. The return response will indicate the contact ID in which you can use on the Create an Engagement endpoint.