A solution would be to have a boolean property to control the editable setting and set the property on click of the button with a section refresh and use the edit options setting on the field's presentation tab to be read-only based on the boolean property value.
For the Section that is Read-only, add a when condition that checks if the button click has been performed. So with the button click, you can run a data transform and set a value for a dummy property. When this property value has been set, make the section editable. You will need a refresh section after running the data transform for the button click.