Marshmallow is traditionally made by stirring a hot supersaturated solution of sugar and gelatine or agar into whipped egg whites. On cooling a material with (at least) four phases present is formed. The phases are:
the protein in the egg and gelatine (or polysaccharide in the agar) form an elastic solid held together by crosslinks between the protein molecules
the excess sugar crystallises to form very small rounded sugar crystals that flocculate and form a weak solid framework
the remaining sugar forms a fluid but very viscous sugar/water syrup
the air bubble originally in the beaten egg white persist in the marshmallow as air bubbles
So your question has no simple answer. A lump of marshmallow is basically solid in the sense that it will not flow under an (small) applied stress. However the structure of the solid may rearrange under stress as the sugar syrup flows, so over time even a small stress may cause a long lived deformation after the stress is released.
For completeness I should note that confectionary manufacturers use as little expensive egg and as much cheap gelatine as they can get away with, which produces a more rubbery texture. The marshmallows your granny makes will stickier but nicer.