Lookup a value (in column) based on "Accumulated Sum" (or total) of QTY shipped column

Staff-A [Column A, row 2] "Fills" a Location with 50 QTY [Column B, row 2] at 12:00 [Column C, row 2]

From 12:05 to 12:30 [Column H] QTY are depleted from the Location [Column G] ...a total of 50 QTY have been depleted at 12:30 (from 12:05 to 12:30)

HOW DO I: "Lookup" the QTY [Column G] and "Intelligently" return the Time value (of 12:30) in [Column H, row 8]

NOTE: 5 QTY at 11:00 [Column G & H, row 2] is ignored - because they were depleted 'before' 12:00 [Column C]

ALSO, HOW DO I: "Lookup" the QTY [Column G] and return the Time value (of 12:20) in [Column H, row 6] ...for Staff B [Column A, row 3] who "Filled" the (same) Location with 20 QTY [Column B, row 3] at 12:15 [Column C, row 3]

VLOOKUP returns the first value (eg: 11:00) - however, I'm not sure how to tell VLOOKUP to 'sum' up the values (to equal the QTY filled) ...and then return that time value

https://docs.google.com/spreadsheets/d/13ymOatgYSTbPsoUddv2sOxtHhJHNtNmz4ldvCJm1uVE/edit

Added More "RealWorld" Data

Indicated in Column G whether [The Result] is correct

UPDATED FORMULA:

=iferror(let(Σ,filter(I:J,H:H=B2), Λ,xmatch(C2,index(Σ,,1),1),
     Ξ,chooserows(Σ,sequence(max(1,rows(Σ)-Λ),1,Λ)),
     xlookup(E2,scan(,index(Ξ,,2),lambda(a,c,a+c)),index(Ξ,,1),,1)))