Is the Universe Eternal?

The short answer seems to be that the Torah is teaching that the Universe had a beginning, but the Torah is not stating the age of the Universe.

The fourth ikar (principle) of the Rambam's 13 principles states that Hashem preceded the Universe and created it ex-nihilo (from absolutely nothing). So the Universe (or the "multiverse" if a multiverse exists) can only have existed for a finite time. In a later version of the 13 principles the Rambam added that this fourth principle is "a great foundation of the Torah of Moshe Rabbeinu".

Until the early 20th Century, many scientists and philosophers argued that the Universe was eternal. The Rambam argued strongly against this prevailing concept of an eternal Universe as this concept would preclude the existence of prophecy or Torah. An eternal Universe would be subject solely to scientific law.

However it does not appear that the Rambam ever stated the age of the Universe. The Rambam states in Moreh Nevuchim 2:13 that the Torah is teaching that the Universe had a beginning, and time itself was created, but we cannot state that the Universe was created at a specific time. This is because a Universe created at a specific time would necessarily invoke a condition of eternal Aristotelian time. Such an eternal Universe precludes the existence of prophecy or Torah. Therefore, according to the Rambam we can't state that God created the world at a particular time.

The Rambam in Moreh Nevuchim seems to be teaching that the six days mentioned in Breisheet are six stages in the creation of the Universe.

In an informative video, Rav David Bar-Hayim explains that the six days mentioned in the first chapter of Genesis do not necessarily correspond to the present periods of time we call days:

"The creation was a process that played out over a period of time, an undefined period of time, clearly the reference in the Torah to six days has to be understood to be six periods or six stages in time...the sun did not exist at the beginning, clearly the day referred to in the Torah is an allegorical or approximation of what is truly meant...we do not know how much time was involved, it may be billions of years...science also understands today that all of reality, the entire Universe came into existence from nothing..." ( Rav David Bar-Hayim, https://www.youtube.com/watch?v=YdvLfJGQYgw )

In the last 100 years, scientists have discovered substantial evidence that this Universe did have a definite beginning. It appears that modern science has actually confirmed some critical Torah concepts that had been challenged in earlier periods of history. "Scientists came to the conclusion that the Universe had a beginning from two separate lines of evidence..." (Interview with Intelligent Design scientist Dr. Stephen Meyer, https://www.youtube.com/watch?v=lHcuZsdv6DE )