Is there a way to assign a default Category to a Post when the user creates a new Post?

WordPress presents default category as a setting in Settings -> Writing (though this doesn’t seem to pre-check the checkbox):

The new_to_auto-draft action will allow you to do things to a new post before the page loads, and does pre-check the checkbox (tested):

add_action( 'new_to_auto-draft', static function ( $post ) {
    $default_category_id = 25; // The ID of your default category.
    wp_set_object_terms( $post->ID, $default_category_id, 'category' );
} );