The behavior where system messages are added to User Notes is a default feature of the User Notes plugin and there currently isn’t a specific site setting or toggle available to suppress system-generated notes, such as those from triggering the min first post typing time system.
A manual workaround for this is to regularly clean up or delete system-generated notes, and you could use a Data Explorer query like this User Notes Report to identify user notes that you want to delete.
With that in mind, if the ability to disable system messages from user notes is a feature you’re interested in, I would encourage you to create a Feature topic in our Meta community. The more people who show interest in a feature, the more likely it is to make it into Discourse. 