Proof of commercial use for Trademark registration by foreign company

Simplest way is a screenshot of your website that has a) the trademark and b) ordering information. BUT, if the only showing of the trademark on that screenshot is the web address itself that probably won't be enough, examiners can say that's merely an address.

Yes, U.S. trademark law maintains a pretty strict definition of use. For goods, the mark must be affixed to the goods as they travel through interstate or foreign commerce. That means that if you are selling wearable devices, the mark must be visible on the devices or their packaging such that consumers notice the mark when purchasing the goods and therefore learn that the mark identifies those particular goods. If you are offering a service, i.e. designing software for the wearable, then the mark must be used in association with the service which could be the mark used in an ad, on a website or in marketing materials advertising and describing your software development service. Since the idea behind a mark is that it identifies the goods/services for a consumer, all of these uses presuppose that the mark is placed prominently where the consumer will readily notice the mark upon making its purchase. Consequently, many non-U.S. trademark applicants may have to line up their U.S. distributors in order to have the evidence of mark usage sufficient to be granted a registration.
However, as a non-U.S. or Swedish entity, you have the ability to avoid or substantially defer this use requirement if you have a Swedish or European trademark registration because the USPTO will grant a U.S. registration based upon the registration of the mark in Sweden or the EU. Evidence of use of the mark can then be deferred until 6 years after the registration date when the USPTO will require evidence of the mark's use in order to be maintained on the Register.
** Please note my answers disclaimer in my bio after the question.