Can We Know The Earth's Age?
There are geneologies built into the narative of the bible and other historical records and dates which we can use to form an accurate timeline of the age of the earth. The accuracy with which we can build this timeline is constrained by the precision of the data we have available in the bible. Using the information found in Genesis and elsewhere and starting the count from the creation of Adam, (IE., 'After Adam' was made on 'Day 6' of creation week) we can get the following timeline, 'AA' (or 'After Adam').
From Adam to the Flood
The timings we're given in the bible genealogies are accurate to
within one year of the event. For instance we know that Adam was
130 years old when Seth was born, but we don't know if he
was 130 and 1 month, or just short of 131, for example. This is true
for all the ages. So when we add up the genealogies, we see that the
Flood happened in the year 1656 AA, plus a margin of less than 10 years,
as we have 10 numbers each with less than a year of uncertainty.
From the Flood to Entering Egypt
We can continue onward with an unbroken genealogy from Shem to Abraham in Genesis 11, and we're given information elsewhere in Genesis to extend the timeline until Israel went into Egypt, when Jacob was 130 years old. Using these figures we find Jacob went into Egypt 642 plus perhaps up to 12 years after the Flood, or 2298 AA plus less than 22 years. The genealogies ends at ths point though, and we need to bring the timeline up to Christ to get a simple means of continuance to the present. So, how can we extend the timeline?
From Entering Egypt to the Exodus
In Exodus 12:40 we learn that Israel was in Egypt for 430 years. This agrees well with Genesis 15:13 where God told Abram that his descendants would be in slavery for 400 years. This did not happen immediately on their arrival in Egypt because Joseph was second in command in the country. The change started some time after Joseph died and their population size seemed threatening to a new Pharaoh. Thus the Exodus happened in 2728 AA, plus, maybe, up to 23 years.
From the Exodus to the Kings
After this Israel wandered in the desert for 40 years, so that they entered the Promised Land in 2768 AA plus up to 24 years. From here the timeline becomes a bit harder to follow. This is because we don't know precisely how long the conquest took, or exactly how long it was before the judges started ruling Israel. We are told how long each judge ruled, and how long each period of peace lasted, but some of these periods overlap with some judges only ruling over part of Israel, etc.
But, knowing that dating would be important God provided a clear
statement in 1 Kings that bridges the gap and allows us to
continue building a reliable timeline. 1 Kings 6:1 says...
So we can safely bypass all the individual judges, Saul and David, and go straight to the reign of Solomon and his starting to build the Temple. And thus Solomon began to build the Temple in 3208 AA, with a margin of less than 24 years.
From the Kings to the Exile
We have to allow for a number of co-regencies when people reigned
concurrently and it's seems that the time from the Temple to the
Exile of Judah is actually around 345 years and not the simple
calculation of about 430 years. This brings us up to 3553 AA.
(Add 85 years to final figures if you use simple calculation for Kings!)
From Creation To Today!
From the very first verse of Genesis, God ensured that we would have a factual account in the bible of how He interacted with man from creation. This means that it gives us historically accurate details, as well as theologically accurate information. In fact, what we believe about God is based on historical claims, so if the history is inaccurate, then the theology must be as well! But, as we can see the biblical authors transmitted early history to us with a tolerance of only 50 years in . God's Word is accurate!
Best wishes for Grace and the Peace of Jesus.