Is it possible to set default values for custom fields in a custom post type while my plugin is being activated?

you can do that on a save_post_ hook
try that :

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

    if (!$update) {

        update_post_meta($post->ID, "cx_number", "default value");

        return;

    }


    if (isset($_POST["cx_number"])) {

        update_post_meta($post->ID, "cx_number", $_POST["cx_number"]);

    }


}, 10, 3);