As the report states, "Earth has had a magnetic core for 4.2 billion years, according to the new study. But until 565 million years ago, long before the dinosaurs arrived and a bit before complex life emerged in the Cambrian explosion, that magnetic core worked completely differently. At that point, there was no inner core."
The major problem is that the 4.2 billion years ago is so close to the alleged 4.5 billion year age for the earth. The earth didn't have a core by age 4.2 billion years (at least not like the present), so a different kind of dynamo mechanism is invoked than the one presently assumed is at work in the core now. That earlier dynamo would have to (1) start the field and (2) bring it up to a strong level within a relatively short time, 0.3 billion years. The problem is the dynamo theories, sustaining and changing them out, i.e. switching how the dynamo works, restarts, decays, restarts, etc.