If you don't want to use comments to determine first reply then I'm not sure how you would do that. Using comments you can use conditions to check if the comment was posted by the Reporter followed by no actions (i.e. exit) or if comment was posted by anyone else then set the first response time (presumably in a custom field). You could further restrict it by only updating the field if the comment poster is the Assignee. I don't know how you would detect if the comment poster was one user in a list of users other than using multiple if/else conditions.
If this is in a service project then you can use a condition that checks if the comment is public so that internal comments don't update the field (assuming that First Response means a response back to the customer).
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