I think that carbon dating grossly exaggerated, because it is a typical secular principle of measuring the past in millions and billions, and trillions and more years, which is perfectly meets secular agenda to discredit a Biblical account of creation of the universe (cosmos) and the Earth.
But lets take a look at the Biblical account of events. What GOD created first, universe or the Earth? According to Genesis, GOD completely formed Earth on the 3rh day (Genesis 1.9-10).
And what about universe (cosmos)? The Cosmos: sun, moon, and stars, were created on the 4th day (Genesis 1.14-19).
So, the conclusion can be made, as it may sounds strange, the Earth was created before the cosmos!
How actually we can count the age of the Earth and the cosmos, from day ONE? I found very interesting material concerning two first days of creation.
(5. *And there was evening. The day, according to the Scriptural reckoning of time, begins with the preceding evening. Thus, the observance of the day of Atonement is to be 'from even into even' (Leviticus 23.32); and similarly of the Sabbath and Festivals.)
The Pentateuch and Haftorahs. Edited by Dr. J. H. Hertz, C.H.)
(5. *Evening... morning. The Hebrew words erev and boker literally mean "sunset" and "break of dawn," terms inappropriate before the creation of the sun on the fourth day.)
Etz Hayim. Torah and Commentary.
(5. **One day. Not an ordinary day, but a Day of GOD (יומו של הקכ ''ה), an age. With Him a thousand years, nay a thousand ages, are but as a day that is past (Psalm 90.4) (2Peter 3.8 A.G). 'Earthly and human measurements of time, by a clock of human manufacture, cannot apply to the first three days, as the sun was not then in existence. The beginning of each period of creation is called morning; its close, evening' (Delitzsh); in the same way, we speak of the morning and evening of life.)
The Pentateuch and Haftorahs. Edited by Dr. J. H. Hertz, C.H.)
So, what the next? The next I started count genealogy (Genesis 5), the life spend of Adam and all the way down to the Great Flood of Noah. Actually many similar calculation have been made by other scholars and my calculations came close to some of other scholars who did the same thing.
THE GENEALOGY OF MANKIND.
The ten generations from Adam to Noah.
(אדם) - Adam: died in the year 930 from Creation.
(שת) - Seth: born in the year 130 from Creation; died in 1042.
After this time, people begin to do evil.
(אנוש) - Enosh: 235. 1140.
(קינן) - Kenan: 325. 1235.
(מהללאל) - Mahalalel: 395. 1290.
(ירר) - Jared: 460. 1422.
(חנוך) - Enoch: 622. 987.
(מתושלח) - Methuselah: 687. 1656
(למך) - Lamech: 874. 1651.
(נח) - Noah: 1056. 1006.
The CHUMASH. The Stone Edition.
Rabbi Nosson Scherman / Rabbi Meir Zlotowitz.
We can also count generations from Shem to Abram (Genesis 11.10-26) according to the life spend of their lives. In total, I come up with approximate number between 12 and 15 thousand years of the total age of the Earth according to this numbers. You can do it yourself, because all the numbers needed are present.
And how old is the universe? According to Genesis, it seems that the Earth a little bit older than the universe (the Earth created on the 3rd day, the universe on the 4th day). What the spend of those first 6 days of creation, no one knows, and the time of them is not given in earthly years, so we can live them behind.
But the most important things here is the precise numbers of life of the first generations, and upon them we can calculate approximate age of the Earth, and subsequently the universe.
