I've been trying to get my Sony A6000 camera to work with any external flash mounted to the hot shoe, but it seems like they all fire right before the shutter opens. I've tried the Sony HVL-F32M and the Godox TT350s, and I have the same problem with both. When in TTL mode, they fire right before the shutter opens which leaves the photo untouched by the flash. When in manual mode, the flashes don't fire at all. Any idea what could be happening?
It sounds like there might be a fault on the camera hot shoe. The HVL-F32M and TT350S should both work correctly on the hotshoe.
Have you done a visual inspection of the camera's hotshoe, particularly where the contacts are at the front edge? You could try using a blower to clear out any possible debris/dust that might be blocking contact. Also check that the flash is seated full forward in the hotshoe.
This sounds like the "extra" contacts on the MIS style hotshoe are connecting (and trigger the ETTL preflash), while the actual big sync contact in the middle isn't (and thus won't trigger the main flash). As mentioned, check whether the center contact is damaged, oxidized, painted, grease coated, smoke coated, dented, worn, out of tolerance.
Also, is there a possibility this camera was ever used with an unsuitable vintage flash (which might have burned out the sync circuitry by putting tens or hundreds of volts into the hotshoe)?