Is it possible to instantiate a new WC_Cart?

Turns out that I was in the incorrect namespace. A new woocommerce cart can be instantiated by

$cart = new WC_Cart();

assuming you’re in the same namespace as the cart, but if you are in a different namespace and suffering the problem I had with my original question, you would change it to:

$cart = new /WC_Cart();

As the / means to check the standard namespace, the same namespace the WC_Cart was declared in.