What were some of the challenges/problems faced by the Americans during the critical period?
I assume that you are asking about the time from the end of the Revolutionary War until the inauguration of George Washington as the first president under the Constitution. This time is sometimes referred to as “the critical period” for the fledgling United States.
During this time, the US faced economic and military crises. It faced foreign and domestic crises. The major domestic crisis was economic. The US economy was very weak. It was plunged into a depression after independence, largely as a result of losing access to British markets. This meant that many Americans were deep in debt. This led to domestic unrest such as that of Shays’s Rebellion.
In foreign affairs, the US was very weak. Barbary pirates captured American sailors and held them for ransom. The Spanish were making trouble with the US over issues of territory in Florida and the Mississippi River area. Most importantly, Britain was causing problems for the new country. It kept forts on American territory. The British in the forts supplied Indians with arms to help them prevent American settlers from moving into what was then called the Northwest.
All of these were major challenges to the strength, prosperity, and viability of the new nation.