The first major challenge that the Puritan colonists faced might be called an environmental challenge. They had to adapt to trying to make a living in a new land with an unfamiliar climate.
The original Puritan colonists' first challenge was the fact that they arrived in Massachusetts in December. This meant that they had to live off ships stores and help from the Indians until they could (again with help from the Indians) grow crops and harvest them. Almost half the colonists died of exposure and disease in that first year.
A second challenge faced was that of dealing with the Native Americans. Although Squanto and the Wampanoags were instrumental in allowing the Puritans to survive, the Puritans soon got caught up in conflicts between various tribes. This led to such conflicts as the Pequot War.
There were many challenges the Puritan colonists faced. One of the challenges dealt with getting to North America. There were severe storms which they faced along the way. Because of the storms, one of the beams of the ship cracked which made some feel the trip could not continue. Even though the trip continued, other problems existed. There were diseases and shortages of food. One person even died. Upon arriving in North America, other issues arose. Because of the storms, the Puritans arrived much later than expected and in a different location. Arriving in November meant food would be an issue. A shortage of food was a big problem. So was disease. A plague swept through the colony, killing many colonists. There was also the concern about dealing with unfriendly Native Americans. Finally, there were some colonists who felt manual labor was beneath their dignity. At a time when all hands were needed to begin the settlement, some of the so called "upper class" didn't feel they should do the work. There were many obstacles which the Puritans faced.