Yes, we can know the will of God
Can we know God's will? This is a question that we have been trying to answer as long as man has worshiped God - meaning that we have tried to answer this for all of human history. If you worship the One True God, the answer is a clear "yes" because we have the Bible.
First, we know what God requires of us. This is plain throughout Scripture, as the Bible is filled with positive commandments of things we are to do and negative commandments of things we are told not to do. The Bible is filled with commandments such as do not steal, do not murder, do not commit adultery, show mercy to widows and orphans, love your wife, discipline your children and so on and so forth.
Second, we know that God is sovereign over all things. We see this truth in Psalm 115:3, Psalm 22:28, Daniel 4:35, Isaiah 46:10, Romans 8:28, Exodus 9:12, Colossians 1:16-18 and many more places in Scripture.
If you are a Christian, there is simply no foundation upon which to base an argument that we cannot know the will of God in a great many things. While God does give us free will, there is no question that we are to use that will to serve Him - though we are incapable of doing so unless we are freed from the bondage of sin through the blood of Jesus Christ.
So what about in everyday life? We know from Scripture that God does intervene in both large and small matters. The first thing that comes to mind is how God obliterated the cities of Sodom and Gomorrah, but there is another striking example in 2 Samuel 21:1-14. God caused a famine in Israel during David's reign as king because of the wicked actions of King Saul. There are examples all throughout Scripture of God punishing wickedness in earthly ways.
But this does not mean all suffering is due to sin. Jesus promised His followers that we would be persecuted for His name's sake, for example. In John 9:1-3, Jesus corrects his disciples in assuming that sin had caused a man to be born blind, pointing out that his blindness was a means to glorify God.
The short answer is, yes, we can know the will of God, by examining His Word. We will not be able to find answers to every single question about things we see happen on this world, but we can apply general principles to understand how we are to respond, both in what we should do and what we may not do. Those who claim we cannot know the will of God are either ignorant of Scripture or they are liars. More often than not, it is the latter.