When creating a Google Sheet widget, you have the option to tick or untick "Is First Column Label".
If you tick it, the widget will show the data from your spreadsheet's first column. If, however, you leave it unticked, the widget will add generic labels. (row 1, row 2, row 3...)
If you don't want the generic data, then tick this button and the first column in your spreadsheet will be the first column in your Google Sheet widget.
NOTE: You cannot physically remove the first column, but can edit your first column in your source spreadsheet (leave it blank or whatever works best for you) and then tick the "Is first column label" button.