From your original post, it sounds like you just wanted a total count, but now it actually sounds like you want a running counter. You can use COUNTIF for that too, you just need to set the range correctly.
Instead of locking the ending row range, use the same row that the formula is in, and allow the end row number to "float".
So, enter this formula in on row 2 and copy all the way down for all rows:
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