I've done a few things with my son who is also about two and a half, and so far he only uses his index finger to play melodies.
You will notice, if you look through the first Suzuki book, that the pieces do not require much stretching of the hands. The left hand - a little, but you can start off with young children by teaching the right hand only for most, or even all, of book one. Then, go back and introduce the left hand. I would try the LH right away, if it were me, though. If a child is interested enough and can understand what to do, they will make it work.
As Elza was saying, they don't have to play legato, so size of keys isn't a problem. But, maybe it would be better with smaller keys, I don't know. You can buy toy keyboards with tiny keys . . . maybe start there. It's not a bad idea. From what I understand about violin, a small child literally cannot hold a full-size instrument at all, let alone play it. They have to have long enough arms to reach to the end of the fretboard (whilst reaching around the neck to press down strings).