Speeding up the load of the main menu JS

Is there a way to get the main menu JS to load a bit sooner?

The site I just built has quite a few child and grandchild items it its menu, so the menu loads fully expanded for a fraction of a sec before JS loads and collapses it. (screenshot)

Normally not a biggie, except we are also using links to anchors (anchors halfway down the page in some cases). That scrolls the user to the location of the anchor before the menu collapses - so, as the menu then collapses and page becomes shorter, a second later the desired content slides offscreen.

It took me a while to realize those two problems are related, but now that I do - is there a way to force the main menu JS to load early, and only the first time the user lands on a site?