The title is my question--does Tor block access to your internet browsing history before you download Tor, or does it block access to your internet use after downloading Tor?
I assume you're talking about Tor Browser here. Tor Browser itself doesn't keep a history of the pages you visited. If it comes to any pages you visit using other browsers, Tor Browser does not try to stop them from storing any history.
If you used another browser for browsing or to download Tor Browser, that history is not removed.