While big companies may have dozens of trademarks, smaller and lesser-known companies can also have valid trademarks, as long as they satisfy the trademark criteria.
Can a large company infringe a smaller company’s mark? Yes! This is sometimes referred to as “reverse confusion,” where the small company is the first user and the large company is the later user. But, there can still be confusion among consumers. The larger company may use its money and resources (like ads) to infiltrate the smaller company’s market with a similar mark on similar goods or services.