Loading responsive menu CSS earlier

When loading any of the pages on my site on desktop, there is a very brief but noticeable moment (especially on slower connections) where the responsive mobile menus appear, unstyled (and thus large and awkward), before the page loads properly. Investigating, I’ve found that the CSS that tells this menu to not appear on desktop loads at the bottom of the page, obviously loading last in line and giving a brief flash of visibility to the menu before the browser is told to hide it.
How can I change this load order so that the CSS is loaded earlier and thus this annoying flash of icons and menus disappears?

The page I need help with: [log in to see the link]