Determining the last row in a single column

How about using a JavaScript trick?

var Avals = ss.getRange("A1:A").getValues();
var Alast = Avals.filter(String).length;

I borrowed this idea from this answer. The Array.filter() method is operating on the Avals array, which contains all the cells in column A. By filtering on a native function's constructor, we get back only non-null elements.

This works for a single column only; if the range contains multiple columns,then the outcome of filter() will include cells from all columns, and thus be outside the populated dimensions of the range.

This will get the last row in a sheet assuming based on column A.

function getLastDataRow(sheet) {
  var lastRow = sheet.getLastRow();
  var range = sheet.getRange("A" + lastRow);
  if (range.getValue() !== "") {
    return lastRow;
  } else {
    return range.getNextDataCell(SpreadsheetApp.Direction.UP).getRow();
  }              
}

This fixes @mrityunjay-pandey partially-correct answer.

To extend this answer to get the last row and column, we can use:

function columnToLetter(column) {
  var temp, letter = '';
  while (column > 0) {
    temp = (column - 1) % 26;
    letter = String.fromCharCode(temp + 65) + letter;
    column = (column - temp - 1) / 26;
  }
  return letter;
}

function letterToColumn(letter) {
  var column = 0, length = letter.length;
  for (var i = 0; i < length; i++) {
    column += (letter.charCodeAt(i) - 64) * Math.pow(26, length - i - 1);
  }
  return column;
}

function getLastDataColumn(sheet) {
  var lastCol = sheet.getLastColumn();
  var range = sheet.getRange(columnToLetter(lastCol) + "1");
  if (range.getValue() !== "") {
    return lastCol;
  } else {
    return range.getNextDataCell(SpreadsheetApp.Direction.PREVIOUS).getColumn();
  }              
}

function getLastDataRow(sheet) {
  var lastRow = sheet.getLastRow();
  var range = sheet.getRange("A" + lastRow);
  if (range.getValue() !== "") {
    return lastRow;
  } else {
    return range.getNextDataCell(SpreadsheetApp.Direction.UP).getRow();
  }              
}

function run() {
  var sheet = SpreadsheetApp.getActiveSheet();
  var [startRow, lastRow] = [2, getLastDataRow(sheet)];
  var [startCol, lastCol] = [1, getLastDataColumn(sheet)];
}