Here is a quick snippet which helps to load the node object based on the URL alias.

//Your custom URL (alias).
$my_url_alias = 'about-me';
// This line will return corresponding system path.
// Lets say, '/node/15' is corresponding path '/about-me'
$path = \Drupal::service('path.alias_manager')->getPathByAlias('/'.$ahurl);
if(preg_match('/node\/(\d+)/', $path, $matches)) {
// This will load the node object.
$node = \Drupal\node\Entity\Node::load($matches[1]);
}

That's it.
Happy Coding :)