I don't think it will help anything if you replace the capacitors now. They are not old, just well conditioned by now. Maybe in ten years think about it. On the other hand there is a good chance to break someting while soldering the caps. Some of the unreplaceable integrated circuits may be harmed, just by electrostatic from soldering near it.
Chinese "developers" never release any schematics, if they do they never match the actual gear or have severe mistakes. Even as this degrades their products to throw away items. I try to explain why. A correct schematic shows in a few minutes which product they have made a copy of and what simple changes they have done to the original design just to bloat the PCB with important looking parts. Like using a zillion of caps where two or a small handfull would do the same and using different types just for the nice looks. The red WIMA copies are a proof of highest workmanship in Chinese minds, many of them, nicely placed in large droves, even better. Same for the usual clones of Nichicon or Elna "for Audio" etc.
In China copying something is paying respect to the real developer, they say. They are not capable to design something from scratch, that is what many others say. In fact it is better to copy a good design than to do an incompetent new one. It is not even illegal to copy some more than 20 year old DAC, amp or whatever design.
Chinese audiophiles always ask where the origin of the design comes from, it must be a well known western developer like Pass, Levinson, Johnson or brands like Krell, Goldmund or whatever. They don't trust their own designers. So to sell something in the own country, it has to be an "improved" copy of some legendary, western construction. A lot is snake oil and myth, this connects the Western and Eastern audiofools.
If you really want to get rid of the thumping noise, there is a simple, reliable solution. Find some ready made PCB with a timer and relais. The relais must short the output to ground directly or through a, maybe 200 Ohm, resistor, directly at the output terminals. If you use a resistor, solder it directly to the post. The timer is started once you switch on the DAC. The relais must be place near the output post, don't run long wires throug the case.
The only problem is to find the signal activating the output and using it to start the timer. It is best practice not to load that signal, so some high impedance switch should be used. I don't know about your abilities in electronics, but you seem to be quite carefull. Better ask here twice than do something "you thought it might work" and break something that can not be repaired.
I like to use the Ali PCB's for TTL signals that are dead cheap and small. Example:
https://de.aliexpress.com/item/1005001700441473.html