How to determine the number of citations an author had on a given date using Google Scholar? Is there a way to learn the number of citations by author on a particular date in the past? For example, how many citations did Author X have on 1/10/18?
Assuming they have a public scholar profile, I imagine the closest thing you can get is  the number of citations the person has at the end of a given year. You can float over a given year to determine citations per year and then subtract the required years from  &quot;all citations&quot;. This will provide a cumulative total for a given year.
For instance, the person below had 1215 - 248 = 967 at the end of 2019. And 1215 - 248 - 245 = 722 at the end of 2018.

You could probably also interpolate specific dates to get an estimate. Note however, that there is a difference between a 2019 citation and a citation received in 2019. For instance, a journal article that is first published online in 2019, but then gets a canonical publication year of 2020, will probably count as a 2020 citation. Google scholar can also vary in how long it takes to index a reference. For instance, by my guess, academics get about 20% of their citations for a given year in the year that follows (i.e., 20% of 2019 citations are added to Google Scholar in 2020).
As far as I can tell, Internet Archive doesn't index Google Scholar pages.