There's no technical reason why you couldn't dig a far larger tunnel, the Greathead shield was 1880 and that's basically all you need for a modern tunnel boring machine.
That's not to say it's practical though. You'd have to go far deeper than the OTL trench miners went, you may still be vulnerable to people listening out for your excavation (you will be deeper, but you will also be noisier), you'll have to start from further back to avoid detection and you'll need some quiet discreet place (middle of largish copse, something like that?) to emerge on the other side. Plus it may take months, maybe years, depending on how far it is from your launch point to the emergence point, assuming of course your opponent has kindly left you one.
So not ASB, it is possible, but really really not a good idea. Maybe if one side accepts very early on in the war that no form of attack is possible against trenches, for some reason ignores tanks or attacks in other theatres and thinks the frontline wont move for years then maybe there is a tiny chance giant tunnels could happen. And then probably not work and end in disaster.