Most API endpoints, including the alerts list, have a filter capability where you can filter on the properties of the objects. Some properties you could use would be acked_epoch, start_epoch, and maybe end_epoch. I don't see any property that gives a timestamp of when the alert severity changed. It's too early in the morning and I can't remember if alerts change severity or if it's actually a new record in the alerts list (with its own corresponding epoch timestamps). I'll have to test it.
You'd use these as filters like this:
/alert/alerts?filter=startEpoch>:1617213624&filter=endEpoch<:1617213800
But you'd replace the numbers with the timerange filters you want. The ">:" and "<:" are "greater than or equal to" and "less than or equal to" respectively.