On a more straightforward note, if you are at Embry-Riddle and you want to get an "in" with a major airline, apply for an internship with the airlines. Those positions are competitive and do not guarantee you a job, but they get you exposure that you can use later (like free training or a guaranteed interview, in some cases).
If you can't get one of the existing internships offered, write or call several aviation companies and ask if you could intern (for college credit) or work there (for pay) for a summer. Make the most of whatever opportunity you are given.
After you graduate, find a job that will get you accumulating hours at a rapid pace. Keep in mind, however, that QUALITY of hours is as important as QUANTITY. Thus, the same number of hours flight instructing is viewed by airlines as better than banner towing, but fewer hours flying night freight (IFR) is better than a lot of hours doing VFR flying.
One possibility for a low time pilot is to head to Alaska for a summer season. Another possibility is to join the Air National Guard. A third is to go fly in a foreign country to build experience.
Notice that none of these suggestions points to a shortcut?