You can unlock extra inventory space shortly after reaching Eos (first planet). After colonizing the planet and choosing between the science or military outpost, you are introduced to the AVP system on the Nexus. You will get AVP points for completing objectives, such as additional tasks and Heleus missions. These can be spent to release additional Cryo pods and earn bonuses. Once you have the ability to waken extra members of the Nexus crew, you can unlock a perk to increase your item limit and carrying capacity. Navigate to the Commerce Pods section of the menu (you are automatically introduced to the menu through story progression), and select "Trade Capacity" to find it.