First of all, Biblical history shows that God revealed Himself to Adam and Noah, among others. Noah was the line of Enoch, who "walked with God". Noah Himself "found grace in the eyes of the Lord."
After the flood, Noah and his family had the knowledge of the one true God. That knowledge would have remained common through to the time of Babel. At that point, the people were "scattered over the face of the whole earth", yet all of these people would have taken with them a general knowledge and understanding of God, who was known by Noah, their common ancestor.
So, all the cultures of the world would have begun with a common basic theology. To varying degrees, this theology would have been distorted by each culture.
In his book, Eternity in Their Hearts, Don Richardson details accounts of tribes which he calls "people of the lost book", who bemoaned the fact that their ancestors had lost the record of God, which may refer to the writings of Adam and Noah. Some hold these to be two of the authors of Genesis, of which Moses was not the author, but the compiler.
Chinese characters actually demonstrate a quite remarkable, even baffling correspondence to the stories in Genesis 1-11. This would fit quite well with the idea that the Chinese came from Babel just like everyone else.
So, all cultures trace their ancestry to Babel and to Noah. They all began with a common theology. Through time, that theology was distorted, but each retains, to varying degrees, shadows of the same root.
Eternity in their Hearts
Additionally, the Scriptures teach that the concept of General Revelation, that God has revealed Himself to them through nature and perhaps through our spirits.
For what can be known about God is plain to them, because God has
shown it to them. 20 For his invisible attributes, namely, his eternal
power and divine nature, have been clearly perceived, ever since the
creation of the world, in the things that have been made. So they are
without excuse. Romans 1:19-20 ESV
The heavens declare the glory of God, and the sky above proclaims his handiwork. Psalm 19:1 ESV
He has made everything beautiful in its time. Also, he has put eternity into man's heart, yet so that he cannot find out what God has done from the beginning to the end. Ecclesiastes 3:11 ESV
So, God has revealed Himself in general revelation to all mankind, so that there will be common understandings among various cultures, since they all receive the same general revelation.
Thus, the commonalities between Christianity and other faiths is quite easily explained. All faiths trace their roots to Noah and His understanding of the One true God, and we all have the same general revelation.
Not All Made Up
The idea that the commonalities necessitate that all religions were made up is quite a stretch. It assumes there really is no God without ever giving evidence to that end. While someone can maintain that opinion, the Biblical accounts provides a solid logical answer to that.
Accepting Christianity as the one true religion
It is inaccurate to suggest that people are only Christians because they inherited this faith from their parents and were indoctrinated into it. In the past half century, Christianity's greatest growth has been in Korea, China, and Muslim countries. There may be as many as 100 million Christians in China today, and the number is growing. They are coming to Christ out of Buddhism and Atheism. Christianity is actually growing quite quickly in Iran now and many other places where people come to faith in Christ even though they risk abandonment from their families and even death in many cases.
That being said, it is really a separate question regarding why Christians believe Christianity is the One true religion. In brief, I would suggest the following "convincing proofs":
The Resurrection of Jesus - Christianity rises and falls on this historical fact. People have suggested very bizarre alternatives to try to explain this away, but all explanation have failed miserably. Nothing else accounts for how a small band of unschooled, ordinary men from a rural area of a no-account country under bondage to the Roman empire turned the world upside down by a teaching they learned from a carpenter, in the face of brutal persecution and martyrdom.
Fulfilled Prophecy - No other holy book dares to predict the future with such precision and accuracy as the Bible. The virgin birth, the year of the Messiah's death, the Deity of the Messiah, the birthplace of Jesus, the four world empires, and many other prophecies all came true.
Miracles - Last, but not least, the dead are raised, the sick are healed, the blind receive sight, the deaf hear... not just in the time of Jesus, but in answer to prayer, people today experience miraculous healing.
The Transformation of People's Lives - No other teaching has shown to transform the lives of so many people so radically. Countless drunkards, prostitutes, murderers, drug addicts, and many others have been delivered from the most destitute of lives to lives of honor and peace. As the song says, "A refuge for the poor, a shelter from the storm, He brings peace to our madness and comfort in our sadness, a Father to the orphan, a Healer to the broken..." Only in the name of Jesus can such things occur.