Why did God make us finite? The lack of knowledge has caused and still causes so much suffering and hardship in our world. Three examples will suffice.
First, we are lacking in our scientific knowledge of our world. In the book The Little Ice Age by Brian Fagan describes the effect changes in climate had on civilization between 1300 and 1850 but the book also describes other causes of the famine and disease that killed millions. The other causes were the lack of knowledge and the lack of coordination among the people of that time. It was not until humans developed new agricultural methods that increased the yields of crops, imported new crops from other lands, and shared that knowledge with others that most farmers moved beyond substance farming and began to produce a surplus which they could sell. Methods of transportation were developed and used to move food stocks from country to country which helped eliminate famine when one country’s crops failed. Governments began to coordinate relief efforts during times of crisis. 
Second, many people lack the knowledge of personal finances. Dave Ramey has built a multi-million dollar company helping people understand how to structure and greatly improve their personal finances and wealth.
Third, we humans obviously lack knowledge on how we relate to each other—just read any newspaper. Also, the Bible has much to say about how we are to treat each other—the Golden Rule, Jesus’ summary of all the Law and Prophets as love God and love your neighbor as yourself, and the definition of love in 1 Corinthians 13. We would not need all this instruction if we already knew how to properly relate to each other.
The only reason I can think why God made us finite is because he sees a need to put us into certain situations to teach us lessons about ourselves and about life. If our knowledge was complete, we would not be in many of the situations in which we find ourselves. Exactly why God structured our lives in this fashion I cannot explain. It makes life somewhat strange as is expressed in the German saying: Too fast old, too late smart. But I guess this is all strange because we are only looking at this one life; we are not looking at eternity; we are not looking at the person we can become.
 Brian Fagan, The Little Ice Age (New York: Basic Books, 2000), pp. 106-112.