You're going to have a hard time pinning this down to a specific component without a circuit diagram. I did find that there's a service manual for this unit: https://elektrotanya.com/marantz_nr1501_ver.5.pdf/download.html

Seems to be legitimate and has diagrams.

I would recommend starting on the output side - is the popping present on every speaker output? Both left and right? Use a very simple speaker for this, one that doesn't require its own power source, just a red and black wire. Also, is the popping present with no input audio?

If you can narrow it to a certain output you can backtrack it to a specific section of the circuit that feeds that output. Alternatively, if it's present on all outputs then it must be a component that is common to all, and therefore behind the area that splits to the different outputs.

An oscilloscope would be handy - you could identify the faulty signal at the speaker output, then check points along the path backward. Half-splitting is your friend. You don't have to buy an expensive piece of lab equipment, a cheap $30-40 digital oscope will be good enough.

Another option would be to throw parts at it. I see units listed for parts on eBay for ~$80. You could try swapping out circuit boards one at a time.

The first image has some white stuff under the large capacitors, but I think it is supposed to look like that, it looks very similar to one of the images in the review.