[{sections:[{fields:[{name:"Date",value:"2020-11-15T15:59:59.999Z"/** this is string*/},{name:"Title",value:"My book"},{name:"Author",value:"Henry"}]}]}]

db.collection.aggregate([{"$addFields":{"sections":{"$map":{"input":"$sections","as":"s","in":{"$map":{"input":"$$s.fields","as":"f","in":{"$cond":{"if":{$eq:["$$f.name","Date"]},"then":{name:"Date",value:{"$toDate":"$$f.value"}},"else":"$$f"}}}}}}}},{$match:{"sections.fields.value":{$gte:new Date("2020-11-01"),$lte:new Date("2020-11-30")}}}])