Amrit Manthan is a symbol of effort of man or effort of the created beings in the nature created by God. In Indian puranas, there are many stories of people doing tapas and get the grace of God. Many of the rishis had the grace of God. Vedas are presented as discoverie of rishis but still as a whole Vedas are given by Vishnu to Brahma. It is in amrit manthan that the created beings go and do a churning of the milk ocean. It symbolizes effort of man to work on nature and get useful things from it. But the work of man does not give only useful things. It gives things which create problems. Like the poison that came out of the churning.
Also, people with all intentions work on the nature. When evil nature predominates, people who want to promote good conduct have to come together, pool their resources and attack the evil doers. From ancient days till day, people are looking for permanent victory of good over evil. But it is not happening. Evil nature resurfaces, strengthens itself and starts troubling many.
Coming back to the main theme of this write-up, Hindus have to reinforce the idea that apart from God's grace through prayers and tapas, there is an alternate way of creating useful things. If one looks at the last 500 years, man made inventions have provided great comforts and increased longevity to human beings. Scientific research is a modern day tapas to understand nature and predict its behaviour. No doubt, many rituals and techniques of religion are found useful by even scientists. One can see the role of God, in Amrit manthan also. He was there as an advisor and also he himself has to take a major role as the support for the churning rod. May be God provides the support whether a human being asks or not. God is there to see that the creation process continues. So whenever a person is trying to do something and obstacles come in his path, God may be helping him.