It all depends on whether Power BI provides a connector to extract he data from Google. There is a Google Analytics connector which allows you to extract Google Analytics data. There are other connectors to extract data from other places in Google but I am not sure what type of data your are tyring to extract.
The bottom line is that if you can import the Google data into a Power BI Desktop project, then you can publish that project and using Power BI embedding to embed the report from that project in a custom application.
If it turns out there is no available connector for the type of data you need to extract, then the next step is to develop a custom connector using the Power Query SDK. That's a pretty big undertaking, but it provides the most flexibility and the ability to import data from a service that does not provide an existing data connector for Power BI.
