[{"customerSchemes":[{"name":"A","startDate":new Date("2021-01-01")},{"name":"B","startDate":new Date("2021-01-05")}]},{"customerSchemes":[{"name":"A","startDate":new Date("2021-02-03")},{"name":"B","startDate":new Date("2021-02-01")}]},{"customerSchemes":[{"name":"A","startDate":new Date("2021-03-05")},{"name":"B","startDate":new Date("2021-03-01")}]}]

db.collection.find({$expr:{$eq:[{$let:{vars:{a:{$arrayElemAt:[{$filter:{input:"$customerSchemes",cond:{$eq:["$$this.name","A"]}}},0]},b:{$arrayElemAt:[{$filter:{input:"$customerSchemes",cond:{$eq:["$$this.name","B"]}}},0]}},in:{$gt:["$$a.startDate","$$b.startDate"]}}},true]}})