Platform migration- will it affect Search Engine Rankings?

Hi all, we are just in the process of migrating our website onto a new platform and wanted to ask about Search Engine Rankings. We were previously on Wix but are now moving to Squarespace, but completely rebuilding the website from the ground up and only copying across a few articles and blog posts we really want, so basically an entirely new website with the same domain name.

Some of the pages on our old website are now doing quite well in Search Engine Rankings but as we are copying these over to the new site and the old one will only be available under Wix's default domain now I wondered if there was a way to prevent our SEO from taking a dive bomb? Is there a way to boost our rankings on the new site or is it literally starting from zero? (Think I read something about robots.txt and XML sitemaps online but it's a bit confusing to me as the index of pages won't be the same after migrating).

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Thanks for all the help! Sorry my SEO knowledge is only quite basic at this point.