Final answer:
The Force.com Metadata API is the appropriate API for creating and managing data models in Salesforce. It provides capabilities for handling the structure of the data model, unlike other APIs which serve different functions such as interacting with records or authentication.
Step-by-step explanation:
The API that can be used to create the data model in the context of Salesforce is the Force.com Metadata API. This API allows you to retrieve, deploy, create, update, or delete customization information, such as custom object definitions and page layouts, for your organization. It is the tool you would use to programmatically manage your Salesforce data model. While the Force.com API (also known as the Salesforce SOAP API or REST API) allows you to interact with the records within the platform, and the Force.com Single Sign-On API is related to authentication, the Metadata API is specifically designed for managing the metadata (structure of the data model).
The AJAX Toolkit for Force.com is also related to the Salesforce platform but is generally used to interact with the platform using JavaScript within a browser, which does not include the creation and maintenance of the data model itself.