No, Google Assistant is not open source, although some related technologies like the open-source Dialogflow Enterprise Edition are available. For example, Google offers an API for developers to create conversational experiences, such as voice apps. Dialogflow is an API that developers can use to create conversational interfaces for websites, mobile apps, popular messaging platforms, and IoT devices.
The Google Assistant is a software suite of tools and services that are available to Google users. It includes the Google Home hardware, Google Voice service, and access to the Google Search engine and Google Now (Google's version of a personal assistant). It works in conjunction with all of Google's other services, and also allows users to interact with third-party services and devices.
Google has made some of the code used to power the Google Assistant available to developers through the Google Cloud Platform. This allows developers to build custom applications and experiences around the Google Assistant. However, developers do not have access to the full code base of the Google Assistant, nor can they modify or redistribute the code.