This article reconciles the Torah with the current age of the universe, and is related.
The answer: NO. The way we may get to the answer, however, is the following article.
So the Big Bang Theory includes the idea that the universe expanded from an initial singularity before which the current laws of physics did not apply, into what became the entire universe (and despite the potentially seemingly negative wording, I highly support this theory). By the way, the word 'theory' does not mean 'guess'. How is this to be reconciled with the Torah? Well, everything about the big bang is mentioned in chapter 1 of Bereshis (Genesis)! I won't go into that, but it is obvious that the Torah speaks of the universe's beginning. This is not a strawman, as I am only referring to a specific group of people who do indeed believe the following garbage: that the big bang theory disproves the possibility of G-d.
Anyway, I believe the main claim of this ridiculous notion that the big bang disproves G-d is that science has not discovered G-d in their calculations of the big bang. What do you expect? To physically find G-d? He is not physical, and thus because science deals with real, physical, observable evidence, it is pseudoscience, not science, that claims that G-d is definitively not real. This, by the way, does not mean that there is no evidence for G-d, just that science cannot DIRECTLY SEE G-d. Also, science being unable to disprove G-d is not proof of G-d, however the same works vice-versa.
A second primary claim that these pseudoscience idiots make is that the supposed pre-big-bang existence conflicts with G-d. Firstly, (I am not actually even close to an expert in this field, and may be wrong about this) the existence of this pre-big-bang state is not at all definitive, and the laws of physics had no bearing then (which reminds me of the Zohar's first chapter, though I am not sure if there is actually any connection). Lastly, THIS HAS ABSOLUTELY NOTHING TO DO WITH G-D'S BEING AT ALL. G-d created the singularity, why couldn't he have created any other entities to accompany it?!?
One individual told me many times of the supposed scientific consensus that the big bang refutes any gods (the claimant may have been saying that the big bang refutes G-d, which was also unsubstantiated). Even if these extremely smart people would say something so idiotic, why does it matter if scientists have an incorrect opinion unrelated to science? This is an argument from authority fallacy, usually involving professionals from one field being believed uncritically in their statements regarding other fields in which they profess incompitence. This statement from this individual was unsubstantiated, and thus, being "science" that has no relation to evidence, but opinion, is pseudoscience.
The main reason this individual claimed that science refutes G-d is because he searched it up on the internet and some scientific website said that science refutes G-d. That is a very direct form of the argument from authority fallacy, claiming that because some authority (real or not) said something, it must be true. This is completely incompatible with the scientific method, turning "science" into another religion where one believes whatever they are told. Science is not a religion (despite what Flat Earthers claim), but pseudoscience is essentially defined as when science becomes religion (this, by the way, does not mean that evidence for a religion's truth that complies with the scientific method is pseudoscience). The individual claimed to not want to be part of any religion, yet was duped into one by pseudoscience and pop-science. People like this may claim to not belive in a higher power, but yet believe in scientists as higher powers.
Conclusion: Finally retreating from that previous tangent, the Big Bang Theory merely answers how the universe began, not why the universe began. Thank you for reading, and may Hashem bless you!