Ghast bombs cannot destroy cobblestone. Try to avoid backtracking when running from a ghast, as netherrack will never naturally extinguish. In addition, if a ghast's fireball collides with an active nether portal, the portal will close.

Can fireballs break cobblestone?

Stone, cobblestone, stone slabs, brick, and other "robust" blocks will be unaffected as they all have resistances of 30, but glass only has a resistance of 1.5, so will be destroyed easily.

Is Cobblestone resistant to ghast fireballs?

Ghasts cannot destroy any blocks with a blast resistance of 26 or higher (eg iron bars, Nether Brick Blocks, or cobblestone).