Making a baby by yourself is possible. at least for species such as stick insects, hammerhead sharks, turkeys. .
who don't necessarily need a male to reproduce. This is what we call parthenogenesis. It's most common among insects such as bees, where a fertilized egg produces a female and an unfertilized egg produces a male.
But we also find it in some vertebrates: whiptail lizards, for instance, have no males. The females have evolved in such a way as to contain all the genetic material needed to reproduce. In other species, male-free reproduction isn't obligatory, but can happen when there is no alternative.
In 2006, Flora, a female Komodo dragon had 5 babies without ever coming in contact with a male. In mammals however, a complete and natural parthenogenesis seems impossible.