At the risk of being banned and denounced by some of my blogs most influential fans, I present a few statements of Chazal that appear to buttress the idea that the universe is much older than 5800-odd years, and that there were cycles of creation before Adam.
Cycles of creation: An open secret?
Ibn Ezra Va'yikra 25:2
Discussing shmita, and the idea of sabbatical cycles, he says: A secret about the age of the universe is alluded to here
Ramban Shmos 21:2
Also discussing shmita, and the significance of seven cycles, he says: And the seventh was chosen for days, for years, and for shmita but it all relates to another matter and this is the secret of the age of the universe (sod y'mos ha'olam)
More than one creation?
R. Joshua b. Levi also said: "When Moses ascended on high, the ministering angels spoke before the Holy One, blessed be He: 'Sovereign of the Universe! What business has one born of woman amongst us?' 'He has come to receive the Torah,' answered He to them. Said they to Him, 'That secret treasure, which has been hidden by Thee for nine hundred and seventy-four generations before the world was created.
Rabbi Shimon the Pious said: "These are the nine hundred and seventy four generations who pressed themselves forward to be created before the world was created, but were not created (Note: If they didn't exist, how did they "push themselves forward?" Were these people created or not? Answer: They existed in a different "world," not in ours, ie: they were a previous, pre-Adam creation. More here
B'rayshis Raba 3:7
...Orders of time existed before creation. Rabbi Abahu said: God went on creating worlds and destroying them, until He created this world and said that it was very good
If a Jew who believes in the Torah thinks that the world was created from primeval matter, and that many worlds, made from the same primeval matter, existed before this one, this would not be considered a flaw in his faith
Evidence of these multiple creations from paleontology
In the year 1807... they found in Siberia... a great elephant... whose skelteon now stands in the Zoological Museum in Petersburg... We already know of a giant creature found in... the city of Baltimore... bones of this creature have been found in Europe, too. This creature had been named mammoth... they have found... iguanodon... whose height was 15 feet, and whose length was as much as 90 feet...there is yet another creature called megalosaurus... from all this it is clear... [citing kabbbalists, Gemarahs, RAbaynu B'chaya, the Ramban, and Ibn Ezra's] that the world has been destroyed and renewed over and over again as many as four times --- Drush Ohr Hachayim, Tiferes Yisroel (Rav Yisroel Lipschutz)
Evidence of these multiple creations from cosmology
According to the master Kabbalist, Rabbi Isaac of Acco, when counting the years of these cycles, one must not use an ordinary physical year, but rather, a divine year (Otzar Chaim 86b). The Midrash says that each divine day is a thousand years, basing this on the verse, "A thousand years in Your sight are as but yesterday", Psalm 90:4 (Bereshit Rabbah 8:2, Zohar 2: 145b, Sanhedrin 97a). Since each year contains 365.25 days, a divine year would be 365,250 years long. According to this, each cycle of seven thousand divine years would consist of 2,556,750,000 earthly years. This figure of 2.5 billion years is very close to the scientific estimate as to the length of time that life has existed on earth. If we assume that the seventh cycle began with the Biblical account of creation, then this would have occurred when the universe was 15,340,500,000 years old. This is very close to the scientific estimate that the expansion of the universe began some 15 billion years ago. ---Sefer Yetzirah, commentary by Rabbi Aryeh Kaplan, published by Weiser, 1997, page 186.
Ok, what about the literal word of the Torah?
The bible does not describe things in terms of objective truths known only to G-d, but in terms of human understanding... The Bible uses human language when it speaks of the "rising and setting of the sun" and not of the rotation of the earth, just as Copernicus, Kepler, and other such scientists, in their words and writings, spoke of the rising and setting of the sun without thereby contradicting truths they had derived from there own scientific conclusions. Loshon benei adam, "human language", which is also the language of the Bible, describes the processes and phenomena of nature in terms of the impression they make on the human senses, without thereby meaning to prejudice, in any manner, the findings of scientific research. ---S.R. Hirsch. Collected Writing, volume 7 (New York: Feldheim, 1992), page 57.