It seems like, surprisingly, OSM doesn't have a well-established tag to encode the start of construction. 🤔🤷‍♂️
The closest I was able to find is construction_start= tag, but according to https://taginfo.openstreetmap.org/keys/construction_start there are only ~200 uses of it world-wide.

So while using that tag wouldn't be wrong, it's unlikely anybody would actually take advantage of that information.. unless there's a massive increase in popularity of this tag.