A quick flick through Alm's A Survey of European Crossbows turns up a late 15th century example, perhaps from Burgundy, equipped with a safety catch. As it had a steel prod and was drawn using a windlass, I would suggest that it was a military, not a hunting, weapon.

W. F. Patterson's A Guide to the Crossbow notes that some Han Dynasty crossbow trigger mechanisms had holes in them that might indicate a safety in the form of a wooden pin that could be pulled out with the aid of a string attaching it to the body of the crossbow, but he emphasizes that this is speculation only.

/u/Valkine may be able to shed more light on the subject.

I can't say when safeties were developed but I can say that they were not standard on medieval weapons. While there are a couple of examples where they were present, medieval weaponsmiths loved to experiment, by and large they are absent from surviving weapons and images of the same.

The primary reason for this is likely that accidental discharge wasn't a huge concern with these weapons. Medieval European crossbow triggers were pretty stiff, there was actually more interest in making the weapons easier to fire rather than harder. Stiff triggers could make for awkward, jolting releases which would in turn seriously impair accuracy. Some steps were taken in the 15th Century to address these problems but it wasn't until the 16th century that complex triggers became fairly widespread.

For early firearms the situation was pretty similar. For most of the Middle Ages when gunpowder existed it was used in artillery, so a safety wouldn't have been standard at all. For handheld firearms the earliest ones were fired by inserted a burning wick or red hot iron into the hole and igniting the powder manually. Without a trigger mechanism there's no need for a safety. Matchlocks could in theory have taken a safety on the trigger, but the greater concern would have been the open pan of powder which could be affected by moisture or any stray flame. It's not until the wheel-lock that you really see a situation where safeties become a priority. Coincidentally, the wheel-lock also saw the invention of the pistol, and while I could speculate that a desire to not have ones pistol fire off in your trousers would hasten the invention of the safety that would be stepping beyond my expertise.

/u/Hergrim has already pointed to two of the best contemporary books on the crossbow. Both of these books include examples of crossbows with possible safeties, but it should be noted that most books on this subject prefer to highlight unique or interesting examples of medieval crossbows even when they don't fit in with broader design trends from that period. That's not a criticism, as someone who has spent the last 4 years generating graphs on over a hundred nearly identical crossbows I fully understand that appeal, just something to bear in mind.

Edit: I should add that I know relatively little about Chinese crossbows.