To advertise the 192.168.1.0/24 network to R2 without sending OSPF packets to SW1, the engineer must configure OSPF in such a way that it includes the network in the OSPF advertisements to R2 but excludes it from being advertised to SW1. This can typically be achieved by manipulating OSPF network types or using OSPF passive-interface commands to prevent OSPF updates from being sent out through the interface connected to SW1.