Follow-up from last month's comment [0]:
A few days after that post, I got an email from a human who had actually read and reviewed my application materials. Very refreshing response and left a great impression. Did not progress further in their process at this time.
I can see how responding individually to a large volume of applications would be very tough to do in a reasonable timeframe.
Total time from my first submission to a human response was 15 days. If that represents a peak period, maybe it's a good upper bound on what to expect. I wonder what the lower bound is.
[0] https://news.ycombinator.com/item?id=12629705