Can I save post meta programatically without setting metaboxes?

You should always use update_post_meta() function because if the term doesn’t exist it will make a call to the add_post_meta() automatically.

The same goes for update_user_meta().

Example if you want to add the meta “City” but you don’t have it in the db you simply make a update_post_meta($city) and in $city you need the post_id and the new value for city.
Like that :

$city = array(
'post_id' => $post_id,
'city' => 'Melbourne'
);

For more information refer to : codex.wordpress.org/Function_Reference/update_post_meta