When a network administrator observes CRC errors on a specific switchport associated with one user, the first troubleshooting step recommended is to replace the user's network cable. CRC errors are often indicative of physical layer issues such as noise, interference, or damaged cables. By replacing the network cable, the administrator can potentially resolve these errors without more drastic measures like replacing hardware components (NIC, switch, or uplink cables), which could be more costly and less effective as initial steps. This approach minimizes downtime and is a cost-effective first step in the troubleshooting process.