HELLO
I don't use Trumpf, only Amada machine
from 1500W to 4000W , mostly alfa/PULSAR
for titanium I use always pure (100%) Argon
Max I already cut is 5mm with good result but just for small
number of parts : less than 10Pcs (PRICE !!)
Normally I cut from 0.5 to 2.5mm for aeronautic parts.
I haven't cut Titanium on a Trumpf Laser but I have on Mazaks (1000/1500 Watts), Amadas (2000-4000 Watts), and Bystronic (4400 Watts) as thin as 0.020 to 0.500". You will need 100% Argon on the thicker stuff, you can cut the thinner with Nitrogen but there will be too much oxidation from it.
How thick can you cut? I would double check with the Trumpf Applications Dept. to get some notes but I would say you can safely cut a thickness below the resonator rating on SS (e.g. 3000 Watts= 3/8 (.375) maximum rating, then 0.25" Titanium.
As the Titanium gets thicker, it gets harder to pierce. Good Luck.