So, try this. We're going to play the "C" chord one octave below middle C. Go ahead, using fingers 5, 3 & 1, with 5 on "C", 3 on "E" and 1 on "G". OK. Now find the "G" key one octave lower. What we're going to do is use that "G" instead! It's OK to do because it does NOT matter what octave we're in to make a chord, just that we use the right keys for the chord: they can be in any octave!
OK: to do that,
place your pinkey (5) on that lower "G",
your index finger (2) on the "C", and
your thumb (1) on the "E", and play the chord.
Switch back and forth between the two ways of playing the "C" chord, and listen closely, until you see (oops...hear) that it really is the same chord, and you understand that it's only the keys that matter, NOT the octave!
Actually you can re-arrange those keys-for-"C" in any order and in any octave you want! And the same goes for all the other chords as well.
And that's exactly what keyboard players do: they have figured out these "re-fingerings" of the two or three chords they're going to play in a song, and do them so that they don't have to move either their hands or their fingers very far to switch chords.
For example, do the "new" "C" we did above: pinkey on "G", index on "C" and thumb on "E". Now, without lifting your pinkey finger, move both your index finger and your thumb one white key to the left: VOILA! the "G" chord! (See, it really is easy!)