The authors of the declaration of independence were influenced by the ideas of direct democracy and republicanism first put forth durning which ancient civilization

Ancient greek civilizations influenced many of the philosophers who influenced the writers of the declaration of independence.

Answer : Ancient Greek Civilizations

The Athenian statesman Solon (640-558 BC) took steps that led Athens in the direction of democracy.  According to the American School of Classical Studies at Athens, "While Solonian reforms did not establish democracy, they were a crucial step on the Athenian road to democracy. Solon's constitution, consisting of moderate redistribution rather than a revolutionary transfer of political power, nonetheless granted important rights to the lowest class of citizens."

Cleisthenes (570-508 BC) is known as the founder of Greek democracy. He aligned himself with the Assembly (of the people) against the aristocracy and managed to impose democratic reforms by means of a new constitution that was approved by the Assembly and implemented in 508 BC. There's much more to the story than that, but we'll keep it brief here.

We might also note that Athens was not fully a democracy.  Athens developed a system that valued philosophy and active political involvement by its citizens.  But it was not a full democracy as we'd think of it today, as those who had a political voice were free men, not women or slaves.  And key Greek philosophers, such as Plato, had criticisms of democracy.  Plato's famous Republic dialogue described an ideal form of government in which the brightest minds would be in the position of governing, a sort of philosopher-kings.