Can the same matter exist in all three states?
Well yes, the triple point describes this condition.
The triple point is (are?) the conditions of pressure and temperature when all 3 phases are at equilibrium. In undergraduate physical chemistry, pressure is commonly plotted against temperature to give a complex phase diagram for a particular substance. Three areas can be identified on the graph: solid; liquid; and gas. High temperature, low pressure regions correspond to the gas, whereas high pressure regions correspond to condensed phases. The triple point will appear somewhere on the graph. For water, it is 273.16 K and 0.006037 atm.