1. Immediately speak to a librarian if the assignment requires research.
Research can be scary. Make your life easier by immediately speaking to a librarian (in-person, chat, Zoom consultation). In only 15-30 minutes, they can make sure you are in the right database(s) with the right queries (not too broad, not too obscure) to find the right material.
2. After speaking to a librarian, immediately review abstracts for likely material, and then download or interlibrary loan the items.
It seems like the vital article you want is the one that needs to be requested from another library, which means an interlibrary loan (ILL) request. That means time spent processing that request. Order early so you have the materials when you are ready to begin.
3. Make an appointment with the Writing Center a week before the item is due. That will be your first draft deadline.
4. Use the Pomodoro technique to do a little each day, such as reading a little or writing a little. Don't intimidate yourself by demanding too much of yourself at one time.