function fillDownData() {

  const sheet = SpreadsheetApp.getActiveSpreadsheet().getActiveSheet();

  // Gets sheet's active cell and confirms it's not empty.
  const activeCell = sheet.getActiveCell();
  const activeCellValue = activeCell.getValue();

  if (!activeCellValue) {
    showMessage("The active cell is empty. Nothing to fill.");
    return;
  }

  // Gets coordinates of active cell.
  const column = activeCell.getColumn();
  const row = activeCell.getRow();

  // Gets entire data range of the sheet.
  const dataRange = sheet.getDataRange();
  const dataRangeRows = dataRange.getNumRows();

  // Gets trimmed range starting from active cell to the end of sheet data range.
  const searchRange = dataRange.offset(row - 1, column - 1, dataRangeRows - row + 1, 1)
  const searchValues = searchRange.getDisplayValues();

  // Find the number of empty rows below the active cell.
  let i = 1; // Start at 1 to skip the ActiveCell.
  while (searchValues[i] && searchValues[i][0] == "") { i++; }

  // If blanks exist, fill the range with values.
  if (i > 1) {
    const fillRange = searchRange.offset(0, 0, i, 1).setValue(activeCellValue)
    //sheet.setActiveRange(fillRange) // Uncomment to test affected range.
  }
  else {
    showMessage("There are no empty cells below the Active Cell to fill.");
  }
}
Copies value of active cell to the blank cells beneath it. 
Stops at last row of the sheet's data range if only blank cells are encountered.

Called from menu option.