Can't find my old notes, but found this graph on a quick google:
https://www.cdc.gov/sids/data.htmNote the decline in SIDS rate, which starts in 1988 (see e.g. https://pediatrics.aappublications.org/content/105/3/650 ), before the recommendation (1992) and "back to sleep" campaign (1994) and though it does track the decline of belly sleeping position, I found in the past graphs of belly sleeping from before 1986 in which it was essentially uncorrelated (or even inverse correlated, if you go back enough - but I don't trust that data).
But what's more alarming, is that although there is a continuing decline in SIDS, if you look at the combined SUID (Sudden Unexpected Infant Death) rate, it is essentially flat since 1996 (following a decline from 1990 as visible in the CDC graph, and which goes much farther IIRC). As a data scientist, this hints either (a) change of classification system that was not properly noted, or (b) that there's an underlying reason which causes infant death, which may manifest in different ways depending e.g. on whether the infant sleeps on their belly or their back.
As a new parent, this was terrifying (is anything really ever safe?) but also reassuring (the expert advice might technically be true, but seems to be useless).
I've found this over and over in many other cases - e.g., statins seem to reduce the change of a heart attack, but do nothing for (or even slightly increase) all cause mortality. Also financial advisers give advice which is technically correct but often useless.
Experts rarely qualify the limits of their advice, and that goes double when it is delivered 2nd hand (by nurses or even doctors who never bothered to look at the data but just parrot the official recommendations).