For new account, automatically Update the custom check-box field to true for User-xx or Account Owner profile-xx and permission set-xx.
Need to implement this Without Code. By using custom settings, how can we achieve this.
You can create a workflow wherein the entry criteria can check if user has required profile of permission; In action you can check the checkbox.
Custom settings will not be usable without using apex code. However, you can use custom labels, if you want to make values configurable.