Can I change the post's created date format?
Yes you can. As an admin you can access "Administration » Configuration » Regional and language » Date and time", where you can define date formats and and display types. The latter you can then use in the "Manage display" part of an entities field configuration, or in the view display options of date fields.

Edit: If that doesn't work (which it doesn't for default node displays) and adding preprocess code is not an option (as the OP declares), another option is to hide the "created by" output (content type settings) and adding an own date field that you can fully control. This one will not, out of itself, be set to the current date when creating a node. Though, that might be an option in the field settings, have to look.

Anyway, code level change would be trivial, but without touching code, this is one of those Drupal WTF moments.