$cat = 5;

$args = array(
    'category' => $cat,
    'posts_per_page' => -1,
);

$cat_args = array(
    'child_of' => $cat,
    'hide_empty' => false,
);

$posts_array = get_posts( $args );

$categories = get_categories( $cat_args  );

foreach ($posts_array as $single_post ){
    $first_letter = mb_substr($single_post->post_title,0,1);
    foreach ($categories as $single_cat){
        if ($first_letter == $single_cat->name){
            wp_set_post_categories($single_post->ID,$single_cat->term_id);
        }
    }
}