testing the site before it’s live

I have a complex issue. I need to set up wp on a client’s site, but they have a current site that is up there until we are done with the wp one. I uploaded and installed wp in the root of their site and did a redirect to their existing site so i could work with the other files. This did not seem to work well because in order to see any of my pages i had to do this: https://www.site.com/index.html/wppagehere in order to see the pages i was working with. The problem started happening when I was uploading things like media files because they were not acting properly. So, we removed the index page and redirect and now i am stumped as to how to test this. Any suggestions?