How to find documents that is equal or includes today in its date range?
Just use ISODate(...) (which is an alias for new Date(...))

You can skip $and, if you like:

{ 
   "startDate": { $lte: ISODate("2020-01-01T00:00:00.000+0000") } ,
   "endDate": { $gte: ISODate("2020-01-01T00:00:00.000+0000") }
}


A more dynamic and easier way would be to use moment.js library:

{
   startDate: { $lte: moment().startOf('day').toDate() },
   endDate: { $gte: moment().startOf('day').toDate() }
}