A baby’s mattress is very different from adults. According to the American and Canadian Pedeatric Associations, a baby’s mattress should be firm, to support their growth and keep them safe. Adults may prefer a harder or softer surface.
It is always recommended to use a new mattress for your baby- as an already used mattress (whether of another baby, or of parents) manifests germs and infections that are unsuited for the delicate new born.
A good baby mattress is breathable, to avoid manifestation of microbes, which is mostly achieved by using breathable and mostly natural materials. Of course, it is important to buy a baby’s mattress from a brand you can trust that will take care of the quality at every stage.