Google Sheets: How to query until reaching a particular sum?


I have a sheet with a lot of data, but to keep this simple let’s say column A has a product, column B has a date, and column C has an integer which can be blank, 1, or an integer greater than 1:

Product  Date      # Sold
Thing1   2020-9-9       1
Thing2   2020-9-9       2
Thing3   2020-9-9       3
Thing1   2020-8-8       1
Thing2   2020-8-8       2
Thing3   2020-8-8       1
Thing1   2020-7-7       2

I need to find the date on which I sold the 3rd-last of that item:

Product  Turn 3 Date
Thing1   2020-7-7
Thing2   2020-8-8
Thing3   2020-9-9

Note that for other reasons I will likely end up with a Query in each cell of the second table anyway, so it doesn’t need to get any more complicated than something like:

=query(Table1!A1:C,"Select min(B) where A='"&A2&"' limit X")

where “X” would be how to limit it to the running total of 3.

Thanks in advance for any ideas!