On this page of the Valheim guide, you will find out whether you can expand your basic inventory and thus gain more item slots.
In many survival games, players can increase the capacity of their inventory or backpack. However, at the time of writing this guide, Valheim doesn't have a way to expand the equipment capacity. From the very beginning, players have only 32 item slots (8 quick access slots).
Not enough inventory space - how to deal with it?
An effective solution to a full inventory in Valheim is to place at least one (preferably several) chests where you can group and store excess items and resources.