<?php
/* Get all categories */
$categories = get_categories();
/* Create empty array */
$categories_order = [];
/* For each category */
foreach($categories as $category) {
  /* Modify WP query */
  $args = array('posts_per_page' => 1, /* Max 1 post */
                'category__in' => array($category->term_id), /* In this specific category */
                'ignore_sticky_posts' => true ); /* No sticky posts */
  /* Get all posts from categories with modifier */
  $posts = get_posts($args);
  /* If there are posts */
  if ($posts) {
    /* For each post */
    foreach($posts as $post) {
      /* Add to array key => value (category id => time published) */
      $categories_order[$category->term_id] = get_post_time('YmdHis');
    }
  }
}
arsort($categories_order); /* Order new array by value */
$categories_order = array_keys($categories_order); /* Remove array values */
/* Function to compare $categories_order with $categories->term_id */
function listcmp($a, $b) {
  global $categories_order;
  foreach($categories_order as $key => $value){
      if($a->term_id==$value){
          return 0;
          break;
        }
      if($b->term_id==$value){
          return 1;
          break;
        }
    }
}
/* Create categories array */
$categories = get_categories();
/* Compare are rearrange $categories accordingly */
usort($categories, "listcmp");

  foreach($categories as $category) {
    /* Loop Here */
  }
?>