View listing page/block relationship configuration
Ok, so Content using field_course_reference (Relate each Content with a field_course_reference set to the content.) was used and required and then Content using field_course_offerings (Relate each Content with a field_course_offerings set to the paragraph.) was used and required using the first relationship. 

This ended up allowing me to filter out and only display courses that had an available offering using Content: Course Reference (field_course_reference) with an operator set to Is NOT empty. I was also able to get the other two filters required to work.

However, I still have an issue where instead of just showing the course once, it displays it as many times as course offerings it has. So say that I have 5 different times the course is offered (The Part-Time Offering [Paragraph] allows for unlimited offering choices), it ends up listing the same course 5 times on my page.

Is there any way for the view to only display each course once, disregarding how many offerings are available for each course?

EDIT: Found the answer to the above. Once I turned on aggregation in the advanced settings, it only displayed each Course once.