Trust is essential in the digital world. It is a critical task to build digital trust for the ongoing digital engineering transformation. Aiming at developing a blockchain-based digital trust mechanism for Cloud Manufacturing or Manufacturing-as-a-Service (MaaS), in this paper, we use the manufacturing of low dead space (LDS) medical syringes through Cloud Manufacturing as a motivating scenario to develop a basic framework. To meet the need of optimally saving Covid-19 vaccine doses to save more lives, the medical device manufacturing community needs to make a swift move to meet the surged need for LDS syringes. Cloud Manufacturing is a form of emerging Digital Manufacturing facilitated with Cloud/Edge Computing, the Internet of Things, and other digital technologies. Cloud manufacturing allows quickly establishing a digital virtual enterprise that pools together various manufacturing resources worldwide to meet the surged needs of products and save cost and time. Trusting the product quality and safety is a significant challenge when using Cloud Manufacturing to manufacture the products. This paper proposes a schema of blockchain-based digital trust mechanisms with examples of using Cloud Manufacturing of medical LDS syringes for the urgent needs of catering Covid-19 vaccination.