I have read that the Big Bang created space-time, but how could this be possible? The Big Bang was itself a singularity, and a singularity is a point in space-time where the curvature becomes infinite. So how could the Big Bang create something without which its existence would not have been possible?
It is impossible to measure anything that happened in the Planck Era, so physicists are unsure whether the universe actually began from a singularity or whether the singularity in the Big Bang theory represents an inability to describe the universe at that time. In fact, "Most physicists believe that this is a mathematical artefact and does not describe what actually happened."
It would be more accurate to say that the Big Bang is the beginning of space-time, than that it "created" space-time.
The Big Bang is a description of how the universe evolved in its earliest stages, not exactly a resolution to why the universe came to be. The latter is really a question for philosophy, not something that can be addressed by science per se. Science informs our philosophy, but does not make philosophical claims.
There are questions on this topic on Physics.SE, but they require a certain level of understanding of the subject matter. Your question has some incorrect assumptions around the Big Bang. One being the definition of singularity - in reality this singularity is a point where certain variables may tend toward infinity, meaning our mathematics breaks down.
And the creation of space-time doesn't require anything to cause it - in fact it specifically implies that in our universe nothing could cause it, as there was nothing before it (there was no before)
If I were you I'd visit Physics.SE and read one of the 700 questions over there on this topic.