This may not apply, though t might is some cases. Where there's proven demand and limited capacity, increasing the capacity would make a road more attractive and the demand will rise to meet capacity.

However in the bicycle infrastructure, we're not dealing with expanding existing bikeway capacity at choke points but discussing if providing bike infrastructure that's more convenient or seems safer (let's not jump off and debate whether it actually is, because that isn't relevant) would induce people to change their lifestyles.

IMO it probably would, but only for those who saw (mental/emotional) barriers removed, or as in the case of NYC bridges actual physical barriers. Otherwise there's no capacity problem, and folks who would want to bike already would be.

As for the actual data, part of the problem is timing. If bike infrastructure made the difference, we'd expect a static or slow growth, with a material increase soon after infrastructure was in place. However, many of the data show the growth trend well underway before the infrastructure was in place which would support the notion that biking leads to infrastructure and not the other way around.

We could go on forever, because there seems to be correlation sometimes, but often not. This shouldn't surprise anybody since the USA is a large and diverse country, and there are significant differences among cities of similar size.