Did you notice any changes in oil pressure before the issue happened, such as the gauge needle bouncing around or twitching?

The pump draws oil from the pan and sends it immediately to the filter. Out of the filter, it travels up a vertical gallery to the right lifter gallery where it spreads throughout the engine. The oil-pressure port near the distributor is at the top of that vertical gallery. If the cannister or spin-on filter clogs, unfiltered oil will bypass the filter and continue supplying the engine with unfiltered oil, so a clogged filter typically won't result in no oil pressure.

If the issue happened out of nowhere and the oil gauge was steady before, I'd examine the oil pump pickup for a clog, the oil pump's male tang to see if it sheared off, and the oil pump drive shaft to see if it failed. There's also a chance the pump itself failed internally from wear, but you will usually see the gauge bouncing for some time prior to the complete failure in cases caused by gradual wear. Note that the a 1958 A318 takes a Melling M51 pump and matching slotted drive shaft and will not accept the Melling M72 and its hex drive shaft.

If it were my car, I'd remove the pump and rear main cap to verify if the engine has the problematic block bypass valve. If it does, the valve has likely deteriorated to where the spring and check ball are missing and the engine's oil has been constantly bypassing the filter. It's a common problem on 1956 - 1961 A-blocks (and Gen I Hemi and Hemi-block polys). The valve wouldn't cause a lack of oil pressure unless it were stuck shut, which I've never seen and would expect the canister filter gasket to blow immediately. While I was in there, I'd remove that block bypass valve and plug the passage, inspect the #5 crank journal and bearing for damage from no oil pressure, and disassemble the oil pump to measure the components for wear and to inspect the pressure spring. The Melling M51 pump is still available new but very expensive compared to the M72.

I have a tech article discussing the oil bypass valve and methods to remove and block it with more details and schematics of the oiling system.