Wild titans can't destroy buildings, I repeat, it can't destroy buildings.
I saw a titan near my base in "the maw", I wanted to test it's damage to my base so I go to the menu and saved my progress. Returned to the game, punched the titan and ran inside my base(yeah I just literally ran). It felt like an attack on titan movie by the way.
I can feel the earth quake as it approached my base, i saw its enormous foot at my open window, I heard it growl like I was an ant who just bit his toe.(which i kinda did)
Then it tried to smash my base, again and again and again, but nothing happened aside from the shockwaves and earthquakes, the base didn't take damage.(except my tames, nothing was left of them).
So I tried one more test, the titan finally stopped attacking, So I got out of my base, ran to the titan, punch him then run back. But this time, I decided to go inside my greenhouse.
And guess what, no damage, I look at it in the eyes and laugh. I was satisfied with my experiment, so I go to the menu and restore my save, returned to the game like nothing happened.
Of course, I got on a PVP server, and I always find these guys. I decided to punch it. I thought it was passive. Nope nope nope and NOPE. It will squish you and as the life is crushed out of you, you realize you’re still a noob.
Easily killable with a wyvern. Lightning and poison easiest down to longer range in attack. Just hover above and light it up :) killed my first today and it didn't touch me once. Just remember to watch stamina ;)