Well, I haven't found a way to do it yet, maybe you could send Google a feature request.
Though I have to say, when you start up Google Chrome in New Tab page, you're not actually loading any web pages so nothing is recorded on your computer, and it doesn't take a second to press Ctrl+Shift+N.
It's the same in Safari. The private browsing mode is always turned off when you open it. The Stealther extension in Firefox, however, remains active after restarting.