Ripe Banana, papaya, avocado are all easy no-cook choices that make great finger food when cut.
Steamed fruits and veggies that you can mash easily in your fingers. Broccoli is a great one! You could also try apple, carrot, potato, anything really. Ripe banana strips are also a fave.
The first finger food I tried my little girl with (other than wafer or puffs)was cucumber and she loved it