Do solids spread outward to fill a container?

The answer depends on the solid.

If you dumped a large solid metal cube into a truck, it would not "spread outward" to fill a container.

If you dumped small BBs (think BB gun BBs) into the same truck, the BBs would spread out & fill the container (if you poured enough of the BBs into the container to fill it). Both are solids, but one solid will not 'spread out' like the others.