How to find the text animator with the earliest keyframe?

My approach to this would be a bit different. Instead of doing the same block of code for each property, I'd make a single function to find the earliest property within a set array of properties, and return that.

Here's my approach:

(function() {
  /**
  * Returns the property in the array with the first key
  *
  * @param {Property[]} properties - Array of properties
  * @returns {Property}            - Property with earliest key
  */
  function getPropWithEarliestKey(properties) {
    var earliestProperty = properties[0];
    var earliestKeyTime = Number.POSITIVE_INFINITY;
    for (var ii = 0, il = properties.length; ii < il; ii++) {
      var prop = properties[ii];
      if (prop.numKeys === 0) {
        continue;
      }
      if (prop.keyTime(1) < earliestKeyTime) {
        earliestKeyTime = prop.keyTime(1);
        earliestProperty = prop;
      }
    }
    return earliestProperty;
  }
  var comp = app.project.activeItem;
  var props = comp.selectedProperties;
  var earliestProp = getPropWithEarliestKey(props);
  $.writeln(earliestProp.name);
})();

Note that I'm just getting the selected comp properties in this use case, but you can replace that with any array of properties.

Also-- while not about the code itself, your code styling is very inconsistent making it difficult to read and work with. If you're having trouble trying to parse where an issue may be, or what code blocks are being triggered, it may be worth cleaning it up to a (much) more readable format in line with code samples you'd see online. The same applies to naming of variables; I'd assume "animRot" would be the rotation animator property, not the number of keys on the property.