Building a new website without affecting the current website (wordpress) until finished?

Building a new website without affecting the current website (wordpress) until finished? Concerned about google web crawling, seo, ssl certificates, wordpress config, etc.

I was advised to create a new subdomain and build the new website there but I have concerns about this approach. After your build your new site (wordpress) on the newly created subdomain how do you redirect the main domain to that subdomain and not break google's web crawling or SSL certificates or anything else?