Idea 1: fingering written on your music is only suggested fingering, it can be changed. Yes, you can experiment with the fingering and you will find there are several options, sometimes better solutions to fingering.
Idea 2: take a look at your hand and fingers. We have 3 long fingers, fingers 2, 3 and 4. Now look at the piano, there are sets of 2 black keys and sets of 3 blacks keys. See how easy it is, which fingers do you think go on the black keys?
The piano was made for the hand.
Long fingers reach easily on the black keys, and the thumb and 5 fingers on the white keys.
Idea 3: The thumb is short and stubby, but can move very easily. The thumb is a pivotal finger and when used as a pivotal finger repositions the hand to move up or down.
Example using the right hand: Play C, D, E, F, using fingers 1-2-3-4. Next, lift your thumb off the key of C, and “pivot” it under your hand and play the key G. Notice your hand position, you now have all of your fingers available to play new keys.
Idea 4: The 5 finger is only used when you finish playing the highest note in the right hand or the lowest note in the left hand. Why? Once you play the 5 finger, the hand is in a difficult position to pivot to a new position.
How to add your own fingering to a song. First, find the black keys and start experimenting with the long fingers. You will use a 2-3- or 4 finger on the black keys.
Next, add your 5 finger on the highest point in your music for the right hand, or the lowest point in the left hand.
Next, add the thumb. Place the thumb in the music at the point you will need to pivot the hand so you can reach notes higher or lower. The 2 finger will fall into place at this point.
If your song has all white notes, place your thumb on the keys needed to pivot the hand up or down.
Yes, this is a thinking process but you can do it. When your hand is comfortable on the keyboard, you will know you have the correct fingering.