Not sure about other control panels but in cpanel you can park the new domain on the old domain/site. It indexes as if the content is it's own. Then begin the process of changing the in bound links. Later just make the old domain a redirect if you want or leave it be. You may also want to change the content itself up a bit to trick google and the IP itself wouldn't be a bad idea.
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PLEASE WAIT WHILE BIDEN ADMIN UNINSTALLS ITSELF.....
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