The next step will then be building an 'Analyzer' to search your bio-fossils for DNA.
These blocks drop a big variety of materials but the ones you're initially going to be after are bio-fossils, which have a 22.5% drop rate. Instead, you need to get to work mining fossil blocks before later unleashing your inner scientist.
Apart from a few living fossils that naturally spawn, such as Coelacanth, you won't find any extinct dinosaurs and beasts roaming around when you load up this mob.