General
I think the easiest way to offer someone access to a specified collection would be to create an Azure Function. From the docs:
Azure Functions allows you to run small pieces of code (called "functions") without worrying about application infrastructure. With Azure Functions, the cloud infrastructure provides all the up-to-date servers you need to keep your application running at scale.
A function is "triggered" by a specific type of event. Supported triggers include responding to changes in data, responding to messages, running on a schedule, or as the result of an HTTP request.
C#
Here's an example of how this might look if you want to query documents by id:
https://docs.microsoft.com/en-us/azure/azure-functions/functions-bindings-cosmosdb-v2-input?tabs=csharp#http-trigger-look-up-id-from-query-string
If you want more complex queries to be executed, take a look at this section of the abovementioned documentation:
https://docs.microsoft.com/en-us/azure/azure-functions/functions-bindings-cosmosdb-v2-input?tabs=csharp#http-trigger-look-up-id-from-route-data-using-sqlquery
So basically this enables you to provide a HTTP endpoint, that's configured to run specific query against your CosmosDB instance.
JavaScript
An example of how to set up a CosmosDB instance and create functions for CRUD operations in JS can be found here:
https://dev.to/vidamrr/cosmos-db-crud-operations-using-azure-functions-4d27