Yes, a topside truck box can be installed without drilling into the truck bed by using alternative mounting methods. These methods include using existing stake pockets, clamps, or specialized mounting kits designed for no-drill installations. 
1. **Stake Pocket Mounting**: Some truck boxes are designed to be mounted using the existing stake pockets on the truck bed. This method involves using brackets or adapters that fit into the stake pockets, allowing the box to be securely attached without drilling.
2. **Clamp Systems**: There are clamp systems available that can secure the truck box to the bed rails. These clamps are designed to grip the bed rails tightly, providing a stable and secure installation without the need for drilling.
3. **No-Drill Mounting Kits**: Some manufacturers offer no-drill mounting kits specifically designed for their truck boxes. These kits typically include brackets, clamps, or other hardware that allows for secure installation without altering the truck bed.
4. **Adhesive Solutions**: Heavy-duty adhesives or industrial-strength Velcro can sometimes be used for lighter boxes, though this method is less common and may not provide the same level of security as other methods.
5. **Bed Rail Systems**: If the truck is equipped with a bed rail system, the box can be mounted using compatible brackets or adapters that attach to the rails.
These methods allow for the installation of a topside truck box without compromising the integrity of the truck bed, preserving its resale value and avoiding potential damage from drilling. Always ensure that the chosen method is compatible with both the truck and the box, and follow the manufacturer's instructions for a secure installation.