Could the Jews begin sacrificing in the temple before the tribulation actually starts?
Yes, there is no scripture that precludes that from happening. In Daniel, chapter eight, we find that the Jews daily sacrifice is taken away, so, from that, we can infer that it had begun again. Basically, the Jews could build their temple at any time and reinstitute their sacrifices anytime between now and the rise of the antichrist. It makes a little more sense to me that they would reinstitute full temple practices before the tribulation period begins. It seems like it would be a difficult timing issue if they had to rush it right at the beginning of the tribulation. That is just my opinion, though.