Yes, a 3 year old can sleep on a memory foam mattress. Memory foam is comfortable and supportive, so it is a great choice for children. It is also hypoallergenic, which is beneficial for those with allergies. However, some memory foam mattresses may be too firm for a 3 year old, so it is important to make sure the mattress is suitable for their age and weight. Additionally, make sure that the mattress is flame retardant and meets the safety standards set by the Consumer Product Safety Commission.