We are a Canadian company so everything has to cross the border from USA to Canada. We followed up with the customs broker, explained the situation and they provided us the emails which they received from the carrier actually hauling the freight.
In the event the shipment remains in the USA, we have contacted the shipper and requested documentation such as the driver signature and company name. Most shippers (responsible ones) list the name of the carrier whom is picking up as well as approx. date/time stamp of loading. This information then further assist in reviewing security footage as most locations these days have security cameras. Then it becomes a google search to find the carrier.
When we sign up a new customer, we actually speak with their shipping receiving team and discuss what they record. In many cases, if they shipper/receiver doesn't practice it already, they will begin taking driver and truck company name as to whom is picking up the freight. It takes no extra time in the process, but could be the difference between losing a load.
