What you are describing is called “reading the PDF in the web browser”. The links JammyDodger shared will assist you to achieve that effect with Discourse.
However, the PDF files are still downloaded to the user’s device; it is cached in the browser as a downloaded resource being shown to the user.
I understand that some folks like offering the option to read in the browser, I know I’ve made use of this in policy-making instances where we had to read a lot of PDFs obtained from public data dumps.
A separate concern is that large PDFs would take up too much for user devices, due to network or storage limitations; the way to address this issue is by creating smaller PDFs or making that information available as text in a topic. 