If you have FileMaker Advanced, you can set up a custom menu where selecting new record performs a script that you design instead of the standard New Record action.
If you do not have advanced, you can't add custom menus to your solution.
A "new record" button on your layout, however, could do what you describe.
What may or may not work is to set up a script to be run "on Record Load".
This script can check a specific field in your record and if it is empty, it's a new record and it can both change layouts and set that field to a value so that future trips of On RecordLoad on that record won't produce this layout change.