Answer in brief
Many Latin American countries follow jus soli: a child acquires citizenship by being born in the country. However, the region has no single law, and national rules contain exceptions, for example for children of foreign diplomats or in certain temporary circumstances.
You cannot apply the Uruguayan procedure to Chile, Brazil, Argentina, or Peru without checking. In addition to the child’s citizenship, birth registration, documents, the parents’ status, and the ability to pass citizenship on to the next generation differ.
Before travelling to give birth, study the constitution and official consular procedure of the country concerned. Separately check healthcare, the parents’ right to reside, and passport procedures: a newborn’s citizenship does not always automatically grant adults legal status.