The browser displays the entire page (using the standard text rendering specified in your stylesheet), then the Cufon script returns and replaces it. Due to the way browsers render pages, as well as the fact that the script is run after the DOMLoaded event of the page, there is no good way to avoid an instant flash of text without changes.
I did not say the “good” way ... there are bad ways to do this, for example, hide text that will be replaced by CSS in your main stylesheet, but this is very bad for accessibility and / or for people who have scripts / flash is off .
This problem is currently one of the known limitations of any script / flash based text replacement methods.
EDIT
There was an article on a 24-way blog post about using data uri with CSS3 @ font-face declaration to avoid "Flash of Unstyled Text". Basically, you insert the font data directly into the stylesheet.
Although not very, it does mean that the font is loaded using CSS and is ready to use immediately. @ font-face is currently supported by Safari and Firefox and will be supported in Chrome 4 (which is coming). Support for IE is limited to the Microsoft EOT format, so I consider it "not supported".
Note: How to use data URIs to avoid flash text of non-styled text
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