If you want your newly-created projects to automatically have assignments, you can do that by creating a project template that has assignments and then creating new projects from those templates. The assignments will pass on too.
To do so, create a project, add the assignments to it and then save it as a template. Check Core Help Center for more on adding project assignments and creating project templates. The project template now holds the assignments and all you need to do is create a new project from this template. Make sure that you select the option Project Assignments under Project Attributes to Copy on the Create New from Template screen when creating the project. This ensures that Core copies the assignments from the template to the new project. Check Core Help Center for more on creating projects from templates.