Check the mattress thoroughly for dust and mold spots. Latex foam is naturally resistant to these particles, so their presence likely indicates the material is not latex foam.
Apply pressure to the upper portion of the mattress where your head rests, then apply pressure to the lower section where your feet go to see if there is a difference. Latex mattresses have significantly more support at the top of the mattress.
Press down on the foam and wait for it to recover its shape. It the foam springs back without delay, it is latex. If not, you will need to continue to check it.
Sleep on the mattress overnight and check the foam in the morning. Latex is not affected by temperature, so the heat of your body will not have affected the shape of the foam by morning.
Set a cup of water on top of the mattress and press down on the foam near the cup. A mattress of latex foam will not absorb the movements you make and will cause the cup to wobble.