Query MongoCollection for data between two Date Strings

Im trying to create a query to search for all collections that are in between of two Date strings, however all my attempts have failed and every time I try a query it always return no results

this is the query im using:

const intialDate = new Date('2024-05-23T06:00:00.000Z');
const endDate = new Date('2024-05-24T20:44:02.172Z');

const dispoquery = this.guestModel.find({
  $and: [
    {
      $or:[
        {
          initial: {
          $gte: intialDate
          }
        },
        {
          end: {
          $lte: endDate
          }
        },
      ]
    }
  ]
}).catch((err) => {
  return err;
})
.then((doc:any)=> {
      return doc
      })

I need all documents that comply this assortment:

intial >= intialDate || end <= endDate 

But I always get no results
this is a sample data of my collection:

{
  "folio": "W1013",
  "nombre": "CArlos",
  "llegada": "2024-05-23T06:00:00.000Z",
  "salida": "2024-05-24T19:52:11.050Z",
  "__v": 0
}

Can someone please tell me what im doing wrong please?