Is it possible to add/tick a category to a post when it is created?

You can add a category on post creation with this code :

$postType = "post";

add_action("save_post_" . $postType, function ($post_ID, \WP_Post $post, $update) {


    if (!$update) {

        // default values for new posts

        $post_categories = [get_option("default_category")];

        wp_set_post_terms(
              $post->ID
            , $post_categories
            , "category"
        );


        return;

    }


    // here, operations for updated posts



}, 10, 3);