The Ruger Hawkeye has a Mauser-like extractor. The Mauser extractor was designed to allow the extractor to snap over a the rim of a cartridge. The trick is to wrap your off-hand fingers around the action from underneath and press on the back part of the extractor with your fingertips. This lifts the font of the extractor a bit, making the 'snap' much easier.
Caveat - It is easier to do this with some rifles, even among Rugers, than others. And you may need strong fingers. I find it much easier just to load rounds into the mag, even when using my rifles as single shots at the range.