Inferring Causal Direction Suppose I have time series data for two variables, X and Y. Assume that I am already convinced that there is a causal relationship between the two, but that I am unsure of the direction. Also assume that there will be a short time delay between cause and effect (here, short means at least an order of magnitude less than the time interval between consecutive data points). Are there any standard/established methods for inferring the direction of the causal effect?
Granger causality seems like a potentially relevant concept, but I have only just heard about that concept and I am uncertain.
$\textbf{Edit}$: I want to clarify the "Assume I am already convinced that there is a causal relationship between the two" portion of my question. Let me give an example:
Early in the COVID-19 pandemic local (to my area) health centers weren't giving out tests because there had been no reported COVID-19 cases in the area. I guess tests were wanted more badly elsewhere. Once they got a few obvious-enough cases (I think they were hospitalizations) there started to be more testing.
Now imagine $X$ is the rate of overall testing and $Y$ is the rate at which we get positive results. We can expect, based on policies like the one I just described, that $Y$ has an affect on $X$. But, we also expect that more testing will just find more cases, so $X$ has an affect on $Y$. The question is: how much each way?
This isn't really the application I'm interested in, but I think it basically illustrates what I mean. When I say I'm convinced, I don't necessarily mean convinced by statistics. There are some situations where some kind of causal relationship is a reasonable guess a priori.

Causal direction, or causal discovery from data is a large research topic.  Causal Discovery Algorithms notebook of Cosma Shalizi given a nice list of approaches. However, one has to distinguish, structure discovery i.e., causal graphs as a separate task than only discovering directions.
A nice overview of, Answering causal questions using observational data,   Memorial Nobel prize of 2021, see here.
