You can use the following code snippet to change the required attribute of the path field in the node form alter in this way:
/**
* Implements hook_form_FORMID_alter().
*/
function example_module_form_node_form_alter(&$form, &$form_state) {
$form['path']['widget'][0]['#open'] = TRUE;
$form['path']['widget'][0]['alias']['#required'] = TRUE;
}
This will keep the path tab open by default and mark the alias field as required.