During the period from the time of Jesus Christ in the first century to the end of the fourth century, a span of under 400 years, there have been 39 legitimate Popes, in sequence, starting with St. Peter the Apostle as first Pope. In those 400 years there were 2 false claimants to the papacy. (False claimants are called "antipopes" but the term is misleading, because it does not necessarily reflect on their theological integrity. It just means that their claim to be Pope was not legitimate per the process).
Now think about this. The United States is currently on President number 43. Now imagine if the Presidency was subordinate to an Emperor who had the power to torture and murder him and all US citizens. During the first 400 years of the Church there were active periods of persecution and martyrdom. So I think this mental exercise gives some valuable perspective that during the first 400 years of its life, the Roman Catholic church had a system of continuity and consistency of faith that yielded 39 legitimate Popes in a row, even as many of them were pursued and martyred... roughly the same number as the US has had of Presidents during this country's entire span of existence thus far.
And if you read the writings of the Popes, bishops or any theologians during that time, (also known as "the Early Church Fathers") what they write is completely recognizable to anyone versed in the faith today, throughout the Church's 2000 year old life as it stands today.