Hi @craftechio_green, welcome to community forums!
I saw that your problem is more related to the connection, however, Live Migrator does not support migrations with CosmosDB as the source because this requires Oplog, which CosmosDB does not have.
The strategy is to import/export or use a tool like Apache Kafka to reduce the impact of downtime. See this link: Migrate from Azure CosmosDB to MongoDB Atlas Using Apache Kafka | MongoDB
I hope it helps you!
Best