There is probably not a single surviving contemporary document describing what the Jews of the time really thought of Jesus.

There isn't a single surviving contemporary document describing Jesus, period, no matter who is doing the writing.

All the gospels were written decades after Christ's death. It's fairly solidly established at this point that Mark was written first, probably from the mid-60's to the mid-70's. Earliest date that any reputable scholar will argue for Matthew being written is around A.D. 70, but it was more likely written around A.D. 80. (there is an extraordinary amount of research done on the authorship of the Gospels, but it's easy to get sources who argue in bad-faith). Luke and John were later still.

Matthew and Luke (I think) clearly show Mark as a common influence, and Mark was pretty much definitely finished after A.D. 70. John is written last of all. If we assume that Christ dies in the year 30-33, that puts almost forty years between the death of Christ and the appearance of the first extant Gospel. If Mark is a contemporary account, the author would have been fairly old. If we assume the author of John to be writing a contemporary account, he'd have been around 80 when he finished if he was 20 at the time of Christ's death.

Far more likely that none of the written accounts were made from witnessing events, and that Mark wrote his gospel from oral sources. In any case, only Mark could credibly be contemporary with the life of Christ...but the early church believed that Peter was the "source" of the gospel of Mark, that Peter had given the eyewitness accounts of Christ's life to the author of Mark. If early Christians didn't think Mark was there and had no problem with Mark being hearsay evidence, and the gospel of Mark never claims to have actually been present for any of the events therein...there are no surviving contemporary accounts of what anyone in the whole damn world thought about Jesus.

(Not a Christian or anything but I like the Bible a whole lot)