Since @Codec and @Deicer have already outlined the passive intake concept, I might just a well share a picture, because this concept have been frequently talked about on Discord in the recent days.
The main idea is to have a self locking geometry where the weight of the stack is used to generate the force for pushing on the cube from the sides and lock it in place. You intake new cubes by lowering the stack on a next cube and then just lift it up with the new cube.
It is possible to make it fully passive by lowering the lift all the way until the side-jaws touch the ground and then drive the robot back, but that introduces a bunch of inconvenient limitations.
Better way is to make it passive intake / active outtake by, let say, pulling on the strings to release the stack.