Here we are looking at complex I from from Thermus thermophilus as featured in this paper:
Symmetry-related proton transfer pathways in respiratory complex I
Because it's bacterial it is all labelled up in Nqo terminology. In mammalian complex I we use Nuo terms, where NuoH is Nqo8, NuoL is Nqo 12, NuoM is Nqo 13 and NqoN is Nqo 14. We can ignore all of the other subunits.
Here are the water channels used to allow protons to move through complex I, red beads being water molecules:
The CoQ binding site (and the NADH dehydrogenase unit) are at the right hand end. What is most important is that the water channels are not all open (hydrated) at the same time. In the resting state the N-side channels are open. A conformational change in Nqo8 is induced by CoQ reduction which opens its water channel and allows a proton to enter from the cytoplasm. This triggers a chain of conformational changes horizontally along the central water channel, moving a proton from right to left within each antiporter-like subunit and which also closes the N-side water channels and opens the P-side water channels, to allow protons to move outwards in to the periplasm. This is their doodle from the discussion:
If anyone goes through the diagram in the sort of detail I did they can see that Nqo13 doesn't make sense because glutamic acid E377 is not a lysine (K abbreviation), which it is in the other two subunits. That messes up all of the charge movements and the inter-subunit electrostatic binding. From Fig 1 section B elsewhere in the paper you can see there is an arginine (R163) just "north" of E377 which might be doing this job by binding to the aspartate (D166) of Nqo12 but I can't see that this is addressed anywhere in the paper. So it's just my guess. Still. The basic concept is pretty convincing.
TLDR: The reduction of CoQ to CoQH2 clunks protons horizontally within the central hydrated channel of each antiporter-like subcomplex from their input zone to their output zone.
We have to bear several things in mind. First is that the system is completely reversible today. As in reverse electron transport using a high membrane potential and reduced CoQ couple to reduce NAD+ to NADH, and generate ROS when NAD+ is all used up... Protons will move inwards from periplasm to cytoplasm as this happens.
Also this is complex I, it is a relatively late addition to modern bacterial metabolism dependent on proton tight membranes and the availability of molecular oxygen.
Third is that our best remnant of LUCA is the Na+ pumping membrane bound hydrogenase of P furiosus and this drives from left to right through an Nqo14/NuoN related subunit (and will almost certainly be equally reversible) to its Na+ channel.
I have some Powerpoint doodles to take this a little further.