"Several fish fossils have been found that demonstrate virtually instantaneous burial. Not only are these fossils perfectly preserved but so is the fish they were eating at the time or the baby they were giving birth to at the time!
There are many places in the world today which cause this. It turns out that the burial isn't instantaneous. Rather, it's "burial with perfect preservation".
Organic matter rains down to the bottom of bodies of water. Organic matter rots, a process which consumes oxygen. And it is eaten by creatures, who of course consume oxygen.
If there is any water flow into the lower region, then the oxygen level down there should be enough to sustain some lifeforms. However, in still water, the deeps only get oxygen by diffusion from the upper layers. Diffusion is slow, and rot consumes the oxygen faster than it can arrive.
In such cases, the oxygen level in the lower water decreases to below a critical threshold, which is about 0.5 part per thousand. The lower water becomes lifeless, and anything which sinks there will not rot or be eaten. It will be preserved until it is eventually buried.
There isn't any fossil that clearly shows a birth in progress. Rather, a big fossil and a little fossil were found together. It could have been a birth. but it's just as likely that the big one was eating the little one. Perhaps it took too big a bite and suffocated. Or, there are several other ways for a fish to die quickly. But whatever the cause of death was, a quick death does not prove a quick burial.
It's easy to haul up a water sample and test it. So, anoxic conditions have been detected at the bottom of many fresh water lakes, in peat bogs, and even in some ocean basins. For example, there's one in the Pacific off Los Angeles, between San Clemente Island and Santa Catalina Island. The basin is about 2000 feet deep. Because of a seasonal rain of dead plankton, the bottom 500 feet have less than the critical amount of dissolved oxygen. Silt is arriving at about a foot per century.
If you find fish fossils in a sedimentary rock, it's too late to measure the water that was involved. But you can check if the layers have no bioturbation, that is, no tracks and burrows left by bottom dwellers. You can also check if the silt was fine, which indicates still water. And you can look for a distinctive foraminifer which today lives only in oxygen-depleted waters. So, it is entirely possible to know that an "instantaneous" burial happened in anoxic water.