The growth of graphene on copper by atmospheric pressure chemical vapor deposition in a system free of pumping equipment is investigated. The emphasis is put on the necessity of hydrogen presence during graphene synthesis and cooling. In the absence of hydrogen during the growth step or during cooling at slow rate, weak carbon coverage, consisting mostly of oxidized and amorphous carbon, is obtained on the copper catalyst. The oxidation originates from the inevitable occurrence of residual oxidizing impurities in the reactor's atmosphere. Graphene with appreciable coverage can be grown within the vacuum-free furnace only upon admitting hydrogen during the growth step. After formation, graphene is preserved from the destructive effect of residual oxidizing contaminants if exposure at high temperature is minimized by fast cooling or if cooling down is performed under the protection of hydrogen. Under these conditions, micrometer-sized hexagon-shaped graphene domains of high structural quality are achieved.