Hyacinth stayed on Dark Continent for 7 years and came to the nearest landmass outside Dark Continent when Ging was 17. They meet at this time (Hyacinth is actually in her 50's at this time, but that's also not true since she never aged past 17)

Ging pestered Hyacinth for 6 months and they explored the Dark Continent for 3 years. During this time, Hyacinth fell in love with Ging in return(Ging was a classic case of love at first sight).
This meant that Ging had already the best time of his life as a hunter in those years exploring the Dark Continent. That's why he is not so obsessed anymore with exploration and adventure when he was at searching for Hyacinth.

Ging was 21 when he had Gon. They were actually in the Dark Continent when they discovered the pregnancy stone and conceiving Gon was both an accident and deliberate on his part. Accident since they never planned to seek pregnancy stone and Deliberate since Ging saw the opportunity to tie Hyacinth to him one step further(Hyacinth also consented to this since she absolutely love the idea of having a family)

This is why Gon have the aura of Dark Continent.

Ging was 3 months pregnant when they decided to come out of Dark Continent at that time. Hyacinth and Ging became friends with Silva when Ging was pregnant. Ging was also glamored to never show his pregnancy and was protected by magic tools so much that a nuclear bomb could drop on him and there will not be scratch on him. This is why Silva never knew about them having a child.

Gon was few months old when Hyacinth was kidnapped by Death/Mort.

Ging actually held onto Gon for a year before dropping him in Whale Island.

Aside from gaining delight in seeing Ging run around like a fool, Death also kidnapped Hyacinth as a form of 'light' punishment for Hyacinth giving birth to life, even though Ging was the one who carried Gon to full term. 12 years are, afterall, a blink for Mort so it's considered a light punishment. It did not expect Hyacinth to actually be angry at it for doing that.

Tldr, Gon is basically a forbidden child and should not exist. Unfortunately(or fortunately??) for the world of Hunter X Hunter, Gon was born.