What a cutie! I've raised some finches years ago after we found them in a blown down nest. I fed them a good quality breakfast porridge, Pro-Nutro. It was a huge mess, but they survived and thrived on it.
It was a little labour intensive and I can vividly remember I getting woken up in the middle of the night by screaming hungry babies wanting food! But it was so rewarding, getting them to the point where we could release them into the wild again.
Good luck with your little one!