This is getting silly now... (Or did it already several pages ago?) I remember that there were goa-flavoured .mods in the tracker scene in 1993-1994. The term "goa" as a genre was barely known back then. However, soft-synths were quite limited so there was plenty of sample ripping from hardware or commercial sources (which in turn were typically hardware-based). Where do you draw the line with "no external synths used"?
One landmark was Propellerhead Software's ReBirth, which was released in December 1996 and made fully soft-synthetic classic goa sound quite easily achievable. I have some tracks from 1997, which indeed credit ReBirth as more or less the only sound source. And you could distribute ReBirth-sequenced files directly too. Those were definitely 100% PC.
It's also known that Shiva Shidapu was releasing tracker music in 1997 and they were hardly the only ones. No idea about all their sound sources, though.
I think I made some pure AdLib FM-synth tracks in the mid-90s. The manufacturer of the original card went bankrupt in 1992 so the hardware option was definitely there earlier than goa as a named genre existed. The sound capabilities were definitely limited, but a 303 is not a strict requirement for producing goa, right?