OK a little more info about this amp. I bought this particular amp off eBay in 2018 to restore and sell. My restoration included new power supply and paper/oil coupling capacitors, new power supply resistors and replacement of other out-of-spec components. Tubes and transformers were tested and replaced as necessary. Voltages verified. I had been restoring A300's for several years as a hobby, selling many on eBay, often to repeat customers. I initially sold it to a repeat customer, he liked it but wanted a little more power so I took it in trade in 2020 for a HK A500 (which I also had restored}. When I had the amp the second time I added the CL90 varistor to reduce in incoming voltage a bit. Went thru the amp, all checked OK sold it the second time in 2022. At that time it had the original 7408 tubes. I see it was sold again. Along the line the 7408's were replaced with 6V6, no problem, same tube. The A300 is a robust amp, HK did not drive them hard and my experience is that the original tubes generally test strong even after 60+ years. With replaced caps and in-spec components, it's common that they work well for decades without issues.
Now, addressing amp hum. The noise floor, ie the hum or hiss from the speakers with volume at minimum, from my experience is present in some level with all tube amps. In vintage tube amps, the noise floor varies by manufacturer and model. I've restored Fisher, EICO, Sherwood, Heathkit, Dynaco and others and I find the A300 to be 'in the middle or average' when compared with other amps of the era. The level of noise floor from an amp is determined by other considerations beside the amp itself. A very major contributor is the speaker selection, specifically the efficiency or sensitivity of the speaker.
Speakers are rated in their ability to produce a given sound level based on the power delivered by the amp. Speaker sensitivity is rated in db (decibel). The higher the db rating the more sound is produced for a given input. What's interesting is that a 3db increase in sensitivity between two speakers resuls in a 50% reduction in the power required for a given sound level form the speaker. Said another way, if speaker a has A sensitivity of 87db and it requires an amplifier output of 10 watts, replacing A with B having a sensitivity of 90db you will have the same sound level with 5 watts of amp output. Makes a good case for high sensitivity speakers when the available power output is relatively low, as with tube amps. So, lets use high sensivity speakers with 'lower' output tube amps. Right? Not necessarily, every silver lining has a cloud. The cloud is that the noise floor will be doubled with a 3db sensitivity in speaker change, so the hum you hear with your ear a given distance from the speaker, a 3db more efficient speaker will double the volume of the hum or hiss.
It's a balance of power required to give good sound vs. noise floor.
Specific to the A300, my experience with it dates to 1963 when I bought a nearly new A300 and used it with my Electrovoice 12TRB speakers which have a high efficiency of about 92 db or so, very efficient. Speaker position in the dorm room was on a table head-height and the hiss was noticeable at about 1-2 feet from the speaker. Replaced them with speakers of 87 db and the hum was nearly eliminated. Currently with A300's I use KLH Model 17's, need to put your ear to the speaker to hear a slight hum. I think the 17's have an efficiency of 87 or so.
Long story, don't over-think or sweat the small stuff, particularly with your A300, it's a very rugged amp, just plug it in, turn it on, sit back and enjoy he music. In it's present condition, it probably will last for decades. If something should happen it's easily repairable. Only suggestion is to turn it off when you are not listening to it, but if you want to play it continuously, it would be very happy as well.