Access to the API in Dev Console requires either System Admin or Developer role. For the Developer role, you have to ensure to be added to at least one product profile for the API.
No other roles are permitted to use the APIs, including other Admin roles like Product Admin, Product Profile Admin, etc.
It sounds like you have access to the Admin Console, but not a full System Admin.
Please work with your organization's system administrators to either upgrade your access or grant you the Developer role.
Something else to note: If Analytics API is already added to a project, it will no longer display. If the Analytics API is missing the correct permissions (using JWT auth), it needs to be removed and re-added with any additional product profiles.