The only solution that doesn't require spinning up a VM, reading all the data and writing it back again is the Azure Data Factory [0]. Which according to Azure's own benchmarks [1] manages to copy only 2MBps between two CosmosDb instances each with 100,000 RUs ("Resource Units"). That's more than half a day for a small 100GB collection.
And in case you're wondering whether 100K RUs is a lot, consider the cost: 5840$/Month for single-region writes. 11680$/Month for multi-region writes [2].
Oh, and as a bonus - can you guess the official procedure for restoring a collection from a backup? [3]:
> If you have accidentally deleted or corrupted your data, you should contact Azure support within 8 hours so that the Azure Cosmos DB team can help you restore the data from the backups.
And yeah, it's 8 hours because they backup the database every 4 hours and keep the last two backup copies [3]
[0]: https://docs.microsoft.com/en-us/azure/data-factory/introduc...
[1]: https://docs.microsoft.com/en-us/azure/data-factory/copy-act...
[2]: https://azure.microsoft.com/en-us/pricing/details/cosmos-db/
[3]: https://docs.microsoft.com/en-us/azure/cosmos-db/online-back...