Yes, you indeed can fetch data from the Google Analytics dashboard using Google Analytics API. You can use either Google Analytics Reporting API or Universal Analytics API, based on your requirements. You need to set up a project on Google Cloud Console, enable Analytics API, and create credentials which will allow your application to access data.
Google provides extensive documentation on how to use these APIs. For instance, you can check out this reporting API guide: https://developers.google.com/analytics/devguides/reporting/core/v4, or this Universal Analytics guide:
https://developers.google.com/analytics/devguides/collection/protocol/v1.
These guides explain the process, from setting up the project, creating credentials, to fetching the reports. They even provide examples of code required. Just make sure you have set the scopes and permissions correctly in the API console and in your Google Analytics account.
However, keep in mind that due to privacy and security reasons, these APIs might not give you access to all the data available on Google Analytics Dashboard. You might not be able to access personally identifiable information of users.