After declaring independence from great britain in 1776, what major obstacle did americans have to overcome to gain independence

Defeating the greatest military power in the world.

Explanation:

At the time, the British appeared unbeatable. They had a history of 100 years of military triumphs and their army was the best in the world. Their soldiers were fully equipped, extremely disciplined, well paid and fed. Their navy controlled the seas and they could raise funds easily. Furthermore, some of those funds were applied to get Hessian mercenaries to attack the Americans.