How to run simultaneously old website index.php with a new website based on Grav's Quark theme?

Hello to everyone.
I have a friend with a very old website and he wants a new one. I will use the blog skeleton based on Quark. But I still need to run his old website based on 2 php files: index.php and articulos.php, in parallel with the new Grav site until I finish passing all his old content to the new website and specially after doing the 301 redirection of all his old dynamic URLs to their corresponding Grav’s URLs, in order to preserve his old Google search position. His domain will browse only his old web site, the Grav site will show if I manually type in the URL the renamed Grav’s index.php file, if possible.

In the documentation, the website migration can be done in 3 different ways, I thing in this case choice No. 2 will help, unless you consider there is a better option:

My question is: since Grav also uses index.php, is there an easy way to temporarily rename Grav index.php to other name until I delete the old website, have all the redirects in the .htaccess and then immediately rename back the Grav’s home page to index.php? or there is a better way?
Thanks for any ideas.

Sorry I didn’t realize that can not be done for several reasons. The most important one is that the old website needs PHP 5.4 and Grav needs PHP 7.3.6+ So I created a temporal sub directory with PHP 7.3.29 for Grav until the new website is complete and ready for publish and all the redirects in place on the .htaccess.
Thanks and regards.