As of now only for the following scenarios, First response can be marked in the SupportCenter application:
from this if you want to mark any other actions in the application as
First Response, we can use a script that automatically adds notes based
on a condition to the request.
2. Under Admin >> Self Service Portal >> Enable First response by default for, check Notes
1) Download the attached zip file and extract the contents in the path SupportCenterPlus\integration\custom_scripts.
3) Configure a Custom Trigger like shown below. Here, the status change is used to mark the first response.