Is it possible to use a static front page?

Yes. You have to create one page per language. Set translations as usual and then go to the WordPress ‘Reading settings’ panel. Check ‘Front page displays a static page’ and choose one of the page you have just created. The language doesn’t matter. You can do the same for the posts page.
Then, if you want that the url looks like http://www.yoursite.com/en/ instead of http://www.yoursite.com/startpage/, go to Settings > Languages > Settings and check the option “The front page url contains the language code instead of the page name or page id” in the URL modifications section.