We always recommend to use child themes except of the parent theme. Child theme will allow you to easily update parent theme without loosing your custom changes.
You can install child theme via copying it into wp-content/themes/ folder. In the same folder you must have parent and child themes. For example themename and themename-child. After that you can activate child theme under “Appearance - Themes” in WordPress admin.
If you run one click installation and activated child theme all settings from Customizer will not be applied. Customizer settings are binded to theme name. Theme name for child and parent themes are different.
After successfily installation of theme please add you custom changes into functions.php and style.css. In the functions.php you can deregiter and register again your new hooks and filters.