This question has the correct answer in the currentjs current API:
moment.localeData('en-us').firstDayOfWeek();
As the OP requested, there is no need for an instance of the moment (), nor is it the ugliness of going to the "beginning", a simple simple use of their localeData.
Please note that you may need to download the + locale + locale file, which is significantly larger (44kb) than just the moment (about 12kb).
It seems that from version 2.2.0 more information can be found in their documents: http://momentjs.com/docs/#/i18n/locale-data/
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