try this script

// ==UserScript==
// @name        reddit archive link
// @include     *://*.google*/search*
// @include     *://*.reddit.com/r/*
// @grant       none
// @version     1.0
// @author      memchr
// @description 6/15/2023, 6:57:32 AM
// ==/UserScript==
function get_archive_href(href) {
  return href.replace(/https:\/\/www\.reddit/,"https://web.archive.org/web/https://old.reddit");
}

if (window.location.hostname.match(/^(\w*\.)?google.*$/)) { // google
  const results = document.querySelectorAll('div.yuRUbf > a');
  results.forEach(e => {
    let href = e.getAttribute('href');
    if (href.match(/reddit\.com\/r\//)) {
      href = get_archive_href(href);
      let archive_link = document.createElement('a');
      archive_link.href = href;
      archive_link.textContent = "archive";
      archive_link.style.marginLeft = "10px";
      e.insertAdjacentElement("afterend", archive_link);
    }
  })
} else if (window.location.hostname.match(/^(\w*\.)?redd.*$/)) { // reddit shit
  const href = get_archive_href(location.href);

  const button = document.createElement('button');
  button.textContent = 'archive';
  button.style.position = 'fixed';
  button.style.bottom = '20px';
  button.style.left = '20px';
  button.style.backgroundColor = '#655CF2ff';
  button.style.color = 'white';
  button.style.zIndex = '9999';
  button.style.borderRadius = '20px';
  button.style.padding = '5px';
  document.body.appendChild(button);

  button.addEventListener('click', () => {location.replace(href)});
}

It will add a link to archive.org next to the reddit Google search result, or a blue link to archive button in the bottom left corner of a reddit page.

Script manager such as violentmonkey is required.