If you use deep learning, the missing parts will be filled with something based on whatever you trained the model on. In other words, the training data won't be dinosaur DNA as we don't have that. At best, during training you can classify some DNA as "more dinosaur" and other DNA as "less dinosaur" and you hope the result will be some extrapolation towards "most dinosaur". Despite the practical limitations, it's certainly an interesting thought.
What if the training set is evolution data? To me CRISPR + Deep Learning seems like a powerful combination. Looking to see some amazing advances in this area.