If you'd feel reasonably safe having your dwarves work outside in a low-savagery area, you're ready for the first cavern layer.
If you'd feel reasonably safe having your dwarves work outside in a medium-savagery area, you're ready for the second cavern layer.
If you'd feel reasonably safe having your dwarves work outside in a high-savagery area, you're ready for the third cavern layer.
That's my basic rule of thumb. Generally, the first cavern layer is actually somewhat less dangerous than a Calm area, the second less dangerous than a Wilderness, and the third less dangerous than Untamed Wilds. If the surface is an undead zone, treat them as as about as dangerous as the evil versions of the same savagery (that's taking into account the extra precautions needed to deal with the walking dead).
The bigger creatures are uncommon-to-rare in the upper caverns and the majority of the creatures in the first cavern will flee from your dwarves unless trapped, so wildlife in the first cavern isn't very dangerous, and there's no chance of goblin ambushes in the caverns, so that's why they're safer. Forgotten Beasts seem to show up earlier and more often than titans and other megabeasts, but if you've got a military capable of handling goblins you've got a military capable of handling most FBs, and you get fair warning when they show up anyway, so they're not actually all that bad.