I assume by "nascimento do século" that one means the time around which a new century is beginning... in which case, a more natural English equivalent would be "turn of the century" rather than "birth".
not necessarily, it could be figurative speech for the most important birth in the century. Like when Jesus was born, it was the birth of the century according to Christians.
Could this also translate to mean a really important birth, say the birth of a future king? It's not just any old birth, it's the birth of the century.
Can any portuguese speakers here clear up whether this is actually a phrase you would hear for "turn of the century", or just one of those duolingo sentences?