In Excel, find first column in row with value > 0 and populate column N with the date listed in the heading row of this first column

In column M of the attached spreadsheet, I have a formula (thanks to this forum) that identifies the last date that each work order was worked on:

=LOOKUP(2,1/(B3:L3<>0),B$1:L$1)

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I now need to identify the earliest date that each work order was worked on in Column N of the same spreadsheet, as follows:

• For each row in Column N in Sheet1 of spreadsheet, find the first column between Col B and Col L that has a value > 0, and then enter the date listed in the heading row of this first column into the cell of the corresponding row under Column N.

I have attached a sample spreadsheet and have populated the desired results in red in Column N, as well as shaded the corresponding 'first column' cells in orange to illustrate what I am after.

Thanks!
Andrea
EE_First_Date.xlsx