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I'm trying to find something similar and here the hint I think might help you. I am still discovering the option. I don't think the REST api allows to search base on dates. You have the recent that can help you, but, I haven't found what's the criteria for recent (is it last day, last week), I think, it's just the order of the output, most recent first, and than you can use the link/next return value to get the next elements until you hit the date you wanted or maximum number of record you wanted.
You will need your js script to make ajax call and loop, unless you have a count return value that is really high but that will affect your performance.
You can use by sort by dateCreatedDesc or latestActivityDesc
Check the content service for more options:
My second though, which I haven't explored yet is the search/contents api you have the after keyword but need to be played with as when I check the Jive Apps api, it required a search keyword but the REST api doesn't say if it is required.