Go from non WP site to WP site on different host but same URL

I have a website that I want to redo in WP. On an entirely different hosting service, Bt IU want the existing UrL to be active on the old server until I get the new site completed.

So I can’t use a subdomain.

I can use a temporary URL, But then want to change it to the permanent URL. Don’t want to change the URL.

There has to be a simple way to do this, but every post I’ve read seems to want to make it more complicated than it needs to be.

DON’T WANT TO MIGRATE – but create a replacement website for an existing one, but do it in wordpress.

Thanks in advance.