It sounds like you'll need to start your training inside the cage before you can move forward with anything outside. Will they take a treat from your hand? With one of my budgies, I would leave some millet in the cage for him to eat and discover that it was an absolutely delicious little snack prize.
Once he recognised and understood that millet was the ultimate treat (in his mind
) I would hold the millet out for him to take. He was still a little afraid of my hand but with patience, the internal battle of hand vs millet was overcome with millet being the winner, so each time he'd come near and have a nibble, I'd click my clicker and then he'd associate click with millet. I'd keep doing then until he felt safe enough that the hand wasn't evil and would hold one hand in front of my hand that held the millet so he had to step up to get the millet.
It was just little steps, building trust and progressing at his pace. As others have said, grabbing your budgie will break any trust and it can be difficult to gain it again. However, they're smart little parrots and all of my budgies have learnt quickly even with different levels of fear and trust. It'll feel so great once you've built a good bond