When a website is rebuilt, what loses rankings is rarely the design. It is the addresses that stop existing. Google had «yoursite.com/services/plumbing» saved, that page now returns an error, and what you had earned is gone.
Before the switch
- List every page on the old site. The sitemap or Search Console will give you this.
- Check in Search Console which pages bring the most clicks and for which searches.
- Keep the text of those pages: if they worked, the new site should still cover the same things.
301 redirects
Every old address must point to its new equivalent with a 301 redirect. That tells Google the page has moved and passes on what it had. If a page disappears with no replacement, point it to the closest page, not the home page.
If you change domain
- Redirect the whole old domain to the new one, page by page.
- Use the «Change of address» tool in Search Console.
- Update the website link on your Google listing and social profiles.
- Keep paying for the old domain for at least a year.
After the switch
- Submit the new sitemap in Search Console.
- Check for 404 errors for a few weeks.
- Make sure the new site does not still have the «noindex» used while it was being built.
Some movement in the first weeks is normal. If after two months you are still well below where you were, something was not redirected.