The valve core needs to be installed to make a normal tire inflation fitting work. But the valve core causes a lot of restriction in the valve stem, slowing the airflow into the tire. The air can't come in fast enough to overcome the amount of air leaking out past the unseated tire bead. The answer is: 1) Remove the valve core so air can flow into the tire unrestricted. 2) Use a free-flowing air nozzle that doesn't have the center pin like a tire inflator. Let the air rush in as fast as it will go. That should do the job. Once the tire bead is seated, let off the air nozzle, and install the valve core and inflate as normal. 3) Have a beer because you deserve it.
You may still have a problem if your compressor is very small and has a very low flow rate/small diameter hose. If that's the case try borrowing a unit with a higher flow rate/bigger hose.