The majestic whale started out looking like a big rat.

all mammals started as rat like, right?

The answer was only recently discovered:

http://www.post-gazette.com/stories/news/science/scientists-draw-tree-to-trace-mammal-evolution-673908/

That article says:

The molecular group generally has claimed the first placental mammal most likely lived 80 million to 100 million years ago, along with dinosaurs.

But the morphology group seems to have won the argument, based on the matrix.

They generally claimed that the common ancestor lived shortly after the Cretaceous-Paleogene extinction event 65 million years ago, when there were massive global extinctions, including dinosaurs, due in large part to an asteroid collision with Earth. Afterward, placental mammals emerged and quickly radiated worldwide.

Here's the database they created: http://www.morphobank.org/