Do not launch the game yet. Immediately install the UPDATE NSP. The installer should recognize it as an "Update" for the existing title ID.
Here’s a helpful, organized write-up for A Hat in Time on Nintendo Switch, focusing on the , updates , and DLC for those who use digital backups (e.g., via custom firmware like Atmosphere). A Hat in Time Switch NSP UPDATE DLC
A Hat in Time on the Nintendo Switch is a comprehensive port of the acclaimed 3D platformer, often bundled or updated to include significant expansions and performance patches. Do not launch the game yet