Take a look at Kafka. When your backend pushes data to MongoDB, have it produce a Kafka message that contains serialized Elasticsearch JSON documents and then use either a bespoke consumer, or kafka-connect-elasticsearch, or logstash-input-kafka to consume those documents and bulk-insert them into Elasticsearch.

Bonus points: it will let you have a standby Elasticsearch cluster in another region you could failover to when needed, perform Elasticsearch cluster upgrades/maintenance without losing data, and more.

Depending on your use case this could be an overkill so YMMV.