Is the earth billions of years old or thousands of years old?

Traditional Proclamation of the Birth of Christ

The twenty-fifth day of December.
In the five thousand one hundred and ninety-ninth year of the creation of the world
from the time when God in the beginning created the heavens and the earth;
the two thousand nine hundred and fifty-seventh year after the flood;
the two thousand and fifteenth year from the birth of Abraham;
the one thousand five hundred and tenth year from Moses
and the going forth of the people of Israel from Egypt;
the one thousand and thirty-second year from David's being anointed king;
in the sixty-fifth week according to the prophecy of Daniel;
in the one hundred and ninety-fourth Olympiad;
the seven hundred and fifty-second year from the foundation of the city of Rome;
the forty second year of the reign of Octavian Augustus;
the whole world being at peace,
in the sixth age of the world,
Jesus Christ the eternal God and Son of the eternal Father,
desiring to sanctify the world by his most merciful coming,
being conceived by the Holy Spirit,
and nine months having passed since his conception,
was born in Bethlehem of Judea of the Virgin Mary,
being made flesh.
The Nativity of our Lord Jesus Christ according to the flesh.

City of God St Augustine Book XII Chapter XII

As to those who are always asking why man was not created during these countless ages of the infinitely extended past, and came into being so lately that, according to Scripture, less than 6000 years have elapsed since He began to be, 

https://www.kolbecenter.org/the-character-of-god-refutes-theistic-evolution/

The Replies of the Pontifical Biblical Commission

On questions of Sacred Scripture

Concerning the Historical Character of the First Three Chapters of Genesis

June 30, 1909 (AAS 1 [1909] 567ff; EB 332ff; Dz 2121ff)

I: Do the various exegetical systems excogitated and defended under the guise of science to exclude the literal historical sense of the first three chapters of Genesis rest on a solid foundation?

Answer: In the negative. 

II: Notwithstanding the historical character and form of Genesis, the special connection of the first three chapters with one another and with the following chapters, the manifold testimonies of the Scriptures both of the Old and of the New Testaments, the almost unanimous opinion of the holy Fathers and the traditional view which the people of Israel also has handed on and the Church has always held, may it be taught that: the aforesaid three chapters of Genesis Contain not accounts of actual events, accounts, that is, which correspond to objective reality and historical truth, but, either fables derived from the mythologies and cosmogonies of ancient peoples and accommodated by the sacred writer to monotheistic doctrine after the expurgation of any polytheistic error; or allegories and symbols without any foundation in objective reality proposed under the form of history to inculcate religious and philosophical truths; or finally legends in part historical and in part fictitious freely composed with a view to instruction and edification? 

Answer: In the negative to both parts.

III: In particular may the literal historical sense be called in doubt in the case of facts narrated in the same chapters which touch the foundations of the Christian religion: as are, among others, the creation of all things by God in the beginning of time; the special creation of man; the formation of the first woman from the first man; the unity of the human race; the original felicity of our first parents in the state of justice, integrity, and immortality; the command given by God to man to test his obedience; the transgression of the divine command at the instigation of the devil under the form of a serpent; the degradation of our first parents from that primeval state of innocence; and the promise of a future Redeemer? 

Answer: In the negative. 

IV: In the interpretation of those passages in these chapters which the Fathers and Doctors understood in different manners without proposing anything certain and definite, is it lawful, without prejudice to the judgement of the Church and with attention to the analogy of faith, to follow and defend the opinion that commends itself to each one? 

Answer: In the affirmative. 

V: Must each and every word and phrase occurring in the aforesaid chapters always and necessarily be understood in its literal sense, so that it is never lawful to deviate from it, even when it appears obvious that the diction is employed in an applied sense, either metaphorical or anthropomorphical, and either reason forbids the retention or necessity imposes the abandonment of the literal sense? 

Answer: In the negative. 

VI: Provided that the literal and historical sense is presupposed, may certain passages in the same chapters, in the light of the example of the holy Fathers and of the Church itself, be wisely and profitably interpreted in an allegorical and prophetic sense? 

Answer: In the affirmative. 

VII: As it was not the mind of the sacred author in the composition of the first chapter of Genesis to give scientific teaching about the internal Constitution of visible things and the entire order of creation, but rather to communicate to his people a popular notion in accord with the current speech of the time and suited to the understanding and capacity of men, must the exactness of scientific language be always meticulously sought for in the interpretation of these matters? 

Answer: In the negative. 

VIII : In the designation and distinction of the six days mentioned in the first chapter of Genesis may the word Yom (day) be taken either in the literal sense for the natural day or in an applied sense for a certain space of time, and may this question be the subject of free discussion among exegetes? 

Answer: In the affirmative.