How do I create a formula that references a worksheet tab without using the
tab's name? I'm using the formula in a different file from the source data
I'm referencing. This source file will be written over constantly with a new
source file. The file name and path will always remain the same, and I
always want to reference the same worksheet tab and cell, but the worksheet
tab's name will change. In other words, I always want my file to reference
cell A2 in the 2nd tab from the left from the source file.

Worksheets can be referred to either by name or index number. Use the index
number to solve your problem.