An hour had passed since we entered the forest. It seemed endless. Either that or we were walking in circles; which was probably the case, as/since I was seeing the same trees over and over again.
Which one is the correct option?
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Since both as and since can serve as conjunctions meaning because, I guess both options are correct. Both words are somewhat more formal than because.
According to a Cambridge Dictionary page on as/because/since, one should prefer because, not as or since, in question sentences proposing a reason for something:
Are you feeling unwell because you ate too much?
But this is clearly not your case.
Sometimes as can be ambiguous because one of its meanings is "at the same time that; while", but this is not your case either.