First: When the GP said 13,000 containers, I presume that's TEU (twenty-foot equivalent unit). A double-stack rail car holds 4 TEU. That means that you only (!) need 3,250 cars to replace the ship. That's a really long train.

What's perhaps more reasonable is to replace it with maybe 20 trains. You could maybe run such trains on a 10-minute headway, so 6 trains an hour, so 3 1/3 hours.

That's to replace one ship.

But it's also if you only have a single track rail line. You could build N parallel tracks along the same route. (This is far more reasonable than trying to build something where you can stack the containers 10 high or something, and then wide enough that it would be stable, and then you have to worry about the load-bearing ability of the track.)

But even if you build all those tracks, then you have the problem of unloading the ship at one end, and reloading a different ship at the other end. You can build enough tracks to get any rate you need, but can you get the load/unload speed?

With a smarter system like ETCS you shouldn't need 10 minutes headway

No I literally mean build a giant wide railroad and make something the size of a container ship, which has the capacity. That's what goes on the rails.

We're talking about Mexico right?

We should probably stick with trains, they can be several km long and it means we don't have to build an entirely new machine with all the new technical challenges that would entail.

Thanks for adding detail, but the idea would be to avoid having to group them into a trains at all -- the containers would powered (like a rail gun) and be "shot" straight through the rail system as they're placed on the track.

Seems like it would be a good test for a theoretical "hyperloop" thing, or a maglev. Hyperloop shouldn't be tested first with humans.