I assume you mean what challenges after they gained independence. They had many internal conflicts. This included fighting about religion. There were also natural disasters. There was the problem of transitioning directly from a dictatorship to a democracy.
The Answer is September 8, 1943
Atahualpa, also Atahuallpa, Atabalipa (in Hispanicized spellings) or Atawallpa (Aymara and Quechua)[2][3] (c.1500–26 July 1533) was the last Sapa Inca (sovereign emperor) of the Inca Empire (Tawantinsuyu) before the Spanish conquest. Atahualpa became emperor when he defeated and executed his older half-brother Huáscar in a civil war sparked by the death of their father, Inca Huayna Capac, from an infectious disease (possibly smallpox).[4]
During the Spanish conquest, the Spaniard Francisco Pizarro captured Atahualpa and used him to control the Inca Empire. Eventually, the Spanish executed Atahualpa, effectively ending the empire. Although a succession of several emperors who led the Inca resistance against the invading Spaniards claimed the title of Sapa Inca as rulers of the Neo-Inca State, the empire began to disintegrate after Atahualpa's death.
The Articles of Confederation was the first written constitution of the United States. Stemming from wartime urgency, its progress was slowed by fears of central authority and extensive land claims by states before was it was ratified on March 1, 1781. Under these articles, the states remained sovereign and independent, with Congress serving as the last resort on appeal of disputes. Congress was also given the authority to make treaties and alliances, maintain armed forces and coin money. However, the central government lacked the ability to levy taxes and regulate commerce, issues that led to the Constitutional Convention in 1787 for the creation of new federal laws.