Do you have a bunch of posts which share the same publish date & time? Do you find the order of your posts shifts around each time a query is run? This can happen after running a mass import of posts. Time Smudge spaces out the publish time randomly over the same/next day giving you a definite value for a buttery smooth, consistent sort order.

time-smudge.php

<?php
/*
Plugin Name: Time Smudge
Plugin URI: https://www.philwylie.co.uk/
Description: Do you have a bunch of posts which share the same publish date &amp; time? Do you find the order of your posts shifts around each time a query is run? This can happen after running a mass import of posts. Time Smudge spaces out the publish time randomly over the same/next day giving you a definite value for a buttery smooth, consistent sort order.
Version: 1.0.0
Author: Phil Wylie
Author URI: https://www.philwylie.co.uk/
License: GPL2
*/

/**
 * Class PW_Time_Smudge.
 */
class PW_Time_Smudge {

	/**
	 * Current version number.
	 */
	const VERSION = '1.0.0';

	/**
	 * Post type.
	 *
	 * Change me to the desired post type.
	 */
	const POST_TYPE = 'product';

	/**
	 * Initialize the plugin by hooking into WordPress.
	 */
	public function __construct() {
		add_action( 'init', array( $this, 'time_smudge' ) );
	}

	/**
	 * Hit example.com/?time-smudge. Use at your own risk. Backup first!
	 */
	public function time_smudge() {
		if ( ! isset( $_GET['time-smudge'] ) ) {
			return;
		}

		$args  = array(
			'posts_per_page' => '-1',
			'post_type'      => SELF::POST_TYPE,
			'no_found_rows'  => true,
			'cache_results'  => false,
		);
		$posts = new WP_Query( $args );
		if ( $posts->have_posts() ) {
			$random_times = $this->random_unique_numbers( $posts->post_count );

			$i = 0;
			while ( $posts->have_posts() ) {
				$posts->the_post();

				$original_timestamp = get_the_date( 'U' );
				$new_timestamp      = $original_timestamp + $random_times[ $i ];
				$new_formatted      = date( 'Y-m-d H:i:s', $new_timestamp );

				wp_update_post(
					array(
						'ID'            => get_the_ID(),
						'post_date'     => $new_formatted,
						'post_date_gmt' => get_gmt_from_date( $new_formatted )
					)
				);

				printf( "Post ID: %s - Original: %s / New: %s\n", get_the_ID(), $original_timestamp, $new_timestamp );

				$i ++;
			}
		}

		echo 'Done.';
		exit;
	}

	/**
	 * Generate array of random unique numbers.
	 *
	 * @author Tony Yau
	 * @link   https://link.from.pw/3bXtQ2u
	 */
	public function random_unique_numbers( $count ) {
		$random_number_array = range( 0, 86400 );
		shuffle( $random_number_array );
		return array_slice( $random_number_array, 0, $count );
	}
}
new PW_Time_Smudge();