I had to go look up velar nasal. I doubled the “g” to try to make it clear that wagen is prounounced vagen with a short a like in English wagon, and not a long a like in wages.
I really know very little about phonetic notation, unfortunately. Sorry!
gg isn’t the ipa notation for the velar nasal, it’s the western transliteration of the usual Greek and Gothic notation for the velar nasal or velar nasal+g. Of course g itself has a ridicouls range of values, from silence in through, to j or y in gif, to zh, to dzh, to g proper…
I sometimes stumble across some alternate spellings, such as British “waggon,” and pronounce them with the velar nasal.