Sunn used a 250µF bypass on an otherwise typical 12AX7 input preamp. They did this on guitar amps as well as bass amps. I suppose they wanted the gain of that stage to be flat for all audio frequencies, even sub audio. I've often wondered why.
I think I have an answer for that.
Short Answer: This was very likely used to eliminate hum in the input stage due to heater-cathode leakage. This is a tube-specific problem, because with time and a big-enough pool of tubes you can select those with the least leakage and hum. However, it is also most-problematic for the first stage because even the smallest hum here gets amplified by the rest of the circuit.
Long Answer:
25μF || 1.5kΩ is -3dB at ~4.2Hz, while 250μF || 1.5kΩ is -3dB at ~0.42Hz. If you're lucky, your hearing goes all the way down to 20Hz, while you can actually see the speaker pump in-out down around 16Hz. Available speakers at the time probably had severe roll-off by 40-50Hz (world-class multi-thousand-dollar headphones today do, too, even the ones which seem to have ample bass). And there's no significant fundamental frequency energy below ~80Hz when playing a guitar. So the cap is at least 100-200 times bigger than it needs to be for full-range reproduction of a guitar signal, yet Sunn and Fender and Marshall used a similar cap in some of their amps.
A designer of the day might use a cap bigger than apparently needed inside a feedback loop, to prevent oscillation. This is a long topic and explanation by itself; however, this stage is also not within a feedback loop, so exclude that as being Sunn's reason for the over-sized cap.
I once had a well-known amp manufacturer contact me regarding a vexing hum problem; forum visitors would know the name and the products. The amp design was based on tweed Fender amps and the manufacturer wanted to shape bass response by using input-stage cathode caps 25μF and/or smaller. Sometimes the amp would have a 60Hz hum that was impossible to locate beyond being at the 1st gain stage (and it obviously wasn't due to the manufacturer's build technique or quality). The manufacturer already used an elevated d.c. voltage for the heaters, but the hum stayed. The mystery hum went away when a 250μF cap was used, as in the Fender 5F6-A Bassman.
There are several mechanisms by which hum can be coupled from the heater into the guitar signal. The heater has to be in thermal contact with the cathode to allow the tube to function, yet it must be electrically insulated. Sometimes this heater-to-cathode insulation is imperfect and current can leak through or around the insulation. This system can be viewed as a capacitor, which is define as 2 conductors separated by an insulator.
The "heater-to-cathode capacitor" and the oversized cathode bypass cap can be viewed as a capacitive voltage divider. The source voltage is the heater a.c. voltage; the "heater-to-cathode cap" is a very small capacitance and is in series with the cathode bypass cap, which completes the circuit from cathode to ground. The cathode itself is the mid-point, or output, of this capacitive voltage divider. In a resistive voltage divider, you reduce output voltage by making the resistance from output to the ground lower. In a capacitive voltage divider, you do the same by making the reactance from output to ground lower, which is done by making the cap value larger.
The heater-to-cathode cap has some very-low capacitance, so it has a high reactance at 60Hz. At 60Hz, the 25μF cap has a reactance of 106Ω; going 10x bigger to the 250μF reduces the reactance by 1/10th to 10.6Ω. And cuts the hum output.
The manufacturer I mentioned was using a proven design and layout, and had tried swapping tubes with no improvement in hum. Tube issues seemed to be ruled out, but there was no reason the amp should hum now when it never did in the past. Turns out that manufacturer bought tubes by the case-load. When the hum went away with the bigger bypass cap, it meant that a whole run of 12AX7 tubes had high heater-to-cathode leakage and many tubes in the batch they had exhibited the problem. The tubes were usable, just not in the 1st gain stage, unless the manufacturer was willing to forego tone-shaping by way of the bypass cap at the 1st gain stage.
Classic amp designs would tend to mitigate 60Hz hum in a guitar amp by purposely using speakers that had poor bass response (in early amps) or by shaving bass response (especially in late 60's-70's amps). Fender also used the 12AY7, which was
marketed at the time for low microphonics and hum. Where 60Hz couldn't be shaved (like the Fender's
Bassman amp), the manufacturer could protect against varying input tube quality by using the oversized cathode bypass on the first gain stage.