That's why I came up with the dokuwiki-downloader script a few years ago.
It's a single PHP script that's only a few kilobytes. You upload it to your web server in seconds and then call it from your browser. The script will then download the DokuWiki archive and extract it for you directly on the server.
Since your server has probably a very fast Internet connection and files don't need to be transferred one-by-one, this is most certainly much faster.
Today I released a new version of it. It's mostly a face lift and and upgrade to newer libraries under the hood. The mechanism is still the same - so you can still follow my old blog post on how to use it.
I reused some mechanisms I created for the DokuWiki Recovery Script I created a while ago. So it has a familiar feel to it.
Here's a quick walk-through, because most of my readers here probably have their wiki set up already.
After the last step you're dropped into the standard DokuWiki installer where you create your super user, etc. On a fast server this whole process will probably take you about a minute or two.