Can I Destroy the Giant Enemy Ship Before I'm Supposed to?

Solution 1:

That is the Ravana-class Shivan destroyer, and no you can not destroy it.

Any ship that is a corvette or higher (destroyers primarily, but also juggernauts) are considered "capital ships" and can only be brought to 10% or less hull by "huge" weapons. These weapons include player-fired torpedoes (such as the Helios) as well as a number of other capital ship weapons such as "beams" and "blob turrets".

You can fire all day at the Ravana with your energy weapons and missiles but it will not fall below 10% hull.

Solution 2:

No. You can't destroy that ship with the weapons you possess at that point in the game. You might be able to take out some turrets or some subsystems, but your missiles and guns won't be able to inflict any damage on the actual part of the ship you need to destroy: the massive spikes which protrude from its hull.