Even though it probably sounds horrible, practice for long enough and you’ll sound more and more like what’s written there without you even knowing it. You can always go back to the sheet music to see how they’re voicing the chords in clever ways that you’re not.
That’s the key: practice, practice, practice. Then, maybe, you may get the feel for it; the euphoria that sweeps over you as you’re playing that tells you you finally got the groove. It happened to me once, about 20 years ago, as I was improvising some blues on the piano. It hasn’t happened since.