Probably when we first started using stone, which would actually last long enough to make it into history.
The very nature of a bridge over a river also means the river is likely to change course and wipe out the bridge and foundations, so it's possible a number of crossings have been destroyed that are older.
We actually have evidence of some of the earliest bridges using wood. It's just that bridge-building, even with just wood, is a massive undertaking. Pile bridges took a while to come about, and even then, it was the use of the arch and corbeled arch which made bridges to pass large rivers practical. Otherwise you're effectively limited to one span from bank-to-bank - ie you can only cross a river as wide as the shortest log used in the construction.
bridges that survived in some form in the archeological record. there were almost certainly bridges - logs, rope bridges, etc., that predated these - but these survived in some preserved form - whether the wood was preserved or the cut stone foundations were preserved - there's evidence.