Feel free to redirect me if this has been answered before, but is there any way to tell when this website is at it's peak of activity?

About 1 to 2 minutes on any given post.

around 4 o'clock.

It does not matter that much, in my opinion.
You might get a bit more views when it's daytime in the US, with mild peaks in the morning / lunch / evening.
But it's not big enough to base your upload schedule around.

There is kind of a diurnal pattern to it, in US time zones. Roughly 75 to 80% of the US population lives in the Eastern (New York, Miami) or Central (Chicago, Dallas) time zones.

I have a copy of the posts file from just under a month ago, which contains the submission time of all the posts on e621. Using the following incantation on it (which only works as well as it does because created_at is the third item in each record)

gives me, 41 seconds later, the following:

.
 316209 00
 288462 01
 276180 02
 267367 03
 268851 04
 250794 05
 218480 06
 191604 07
 163027 08
 154322 09
 144858 10
 150010 11
 161907 12
 182326 13
 200682 14
 228790 15
 243447 16
 261349 17
 276883 18
 284440 19
 296221 20
 311422 21
 317284 22
 306736 23

The first big number is the post count, and the second small number is the hour-of-day, in GMT/UTC on a 24-hour clock (so 00 = midnight, 06 = 6 AM, 12 = noon, 18 = 6 PM).

The most popular hour is 22:00 GMT, followed by 00:00 GMT and 21:00 GMT. The least popular hours are 10:00 GMT, 11:00 GMT, and 09:00 GMT.

Translating those to US Eastern, and accounting for both standard and daylight time, the most popular hours are 4 PM to 6 PM, and then 7 PM to 8 PM, US Eastern. The least popular hours are 4 AM to 7 AM, US Eastern.

Translating those to US Central, and accounting for both standard and daylight time, the most popular hours are 3 PM to 5 PM, and then 6 PM to 7 PM, US Central. The least popular hours are 3 AM to 6 AM, US Central.

====* The More You Know