There is no way in NetSuite to know when (Date/Time) inventory allocations happened?

There is. Press history on the item line. If you want to make a saved search, do a transaction search and join to system notes line fields. Select field ”allocated”

That field is not available for me in a transaction search, I will try a System Note Search

Do you find line system note from transaction?

Not for what I need, I'm able to get Allocated Supply with a System Note search, however, not able to get the Line ID or Line Item, I'm trying with SUITEQL now... but I think I'm will end up having to write some code.