You can copy across your existing website to Simba Hosting’s computers and thoroughly test it before “flicking the switch” to make the version at Simba the “real” one that the Internet sees.
Your setup e-mail will have given you the details of how to upload your content to Simba, and how to view it before your domain name is transferred.
If this is done, then there will be no time during which your website is not available. However, if your website is database driven then you may need to take the old version off the Internet to avoid problems with having two different versions of your database existing. If your website does not use any database then there will not be any issue of this kind.