I give my ideas about inventories, even if it's not only the UI.
I saw that there were already a certain number of blocks and I think that the size of the inventory could be related to the number of blocks in the game (more blocks there are, more inventory will be large (with a max limit of course)).
A quick access bar with a dozen boxes
A search bar to discover and search all tons of cubes (proposed by Yonben)
Store things into lockable containers (proposed by PrezidentRedz)
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