The trucking company is liable as the truck's owner, and the company's owner or manager must ensure that the drivers they hire are qualified to drive. Additionally, vicarious liability refers to a business's liability for their employee's actions during their employment. Many drivers do not work directly for a company but work as owners/operators.
You might seek compensation from other sources of liability instead of, or in addition to, the truck driver and the trucking company that employs them. Examples include the manufacturer of defective parts used on the truck or another vehicle involved in the accident, other drivers, or the entity or individual tasked with providing service on the truck.