There are a 3 ways you could do this:
1) Depending on your Google Analytics setup, you can access the following object via Chrome console and pass in your GA property ID:
Object.keys(window.gaData["YOUR-GA-PROPERTY ID"].experiments).forEach(function(key, index){
var value = window.gaData["YOUR-GA-PROPERTY ID"].experiments[key];
console.log("Info", key, value, index);
 });
2) As someone has already pointed out, you can access the _gaexp cookie, which stores your experiment ID and variant number.
    //READ THE COOKIE
    function readCookie(name) {
    var nameEQ = name + "=";
    var ca = document.cookie.split(';');
    for(var i=0;i < ca.length;i++) {
       var c = ca[i];
       while (c.charAt(0)==' ') c = c.substring(1,c.length);
       if (c.indexOf(nameEQ) == 0) return c.substring(nameEQ.length,c.length);
   }
   return null;
   };
   // GET THE COOKIE
   let getCookie = readCookie("_gaexp");
   console.log('getCookie', getCookie);
   // WILL RETURN A STRING IN THIS FORMAT
   // GAX1.2.YOUREXPERIMENTID.18803.0
   // The long number in the middle is your experiment ID
   // The number at the end is your variant number (0)
   // SPLIT THE COOKIE
   let splitCookie = readCookie("_gaexp").split("!");
   // SPLIT THE COOKIE SO YOU CAN ACCESS THE EXPERIMENT ID AND VARIANT NUMBER
3) And lastly, you could use your dataLayer.
A bit more of a clunky way to do it, but in Optimize 360, you could add JavaScript in each variant, (when you go edit your AB Test/variants).  And send your experiment ID to your dataLayer, as well as other information.
EG:
function returnDate() {
  var today = new Date();
  var dd = String(today.getDate()).padStart(2, '0');
  var mm = String(today.getMonth() + 1).padStart(2, '0'); //January is 0!
  var yyyy = today.getFullYear();
  
  today = mm + '/' + dd + '/' + yyyy;
  return today;
}
var dateToday = returnDate();
var ABTest = {
      id: 'YOUREXPERIMENTID',
      name: 'Title of your test',
      description:  'Test description',
      date: dateToday, //The launch date of AB Test.
      variant: 1,
      totalVariants: 5
  };
// AND THEN PUSH ALL THAT INFORMATION INTO THE DATALAYER 
dataLayer.Tests.push(ABTest);
Then to access all that information, all you need to do is access the window.dataLayer object.
Now how I've used google tag manager, add the "Test" key, in dataLayer.Tests. But of course you don't need that, but I just like to organise my object :)