At around 11:10 in the 2nd episode of Golden Kamuy, when asked by Ogata his motivation to hunt for tattoos, Sugimoto says he does it for the girl he loves. There are at least two candidates I can think up.
Umeko, the blind widow of Sugimoto's childhood friend Toraji, who is also Sugimoto's childhood friend. Toraji died in war, before which he pleaded Sugimoto to collect the money for his widow's eye surgery. If this is the case, it's kind of weird -- Sugimoto shamelessly admits that he loves his best friend's wife.
I want a good doctor to take a look at Umeko's... At my wife's eyes.
Asirpa. Asirpa thinks that her dad was killed by Noppera-bou, so she wants to collect all the tattoos to avenge his dad. This is revealed at the end of the first episode, where Sugimoto promises to help her.
The government won't want him killed until they've found it.
Finding the gold is a way to avenge your father's death.
However, it has never been said explicitly who's the girl Sugimoto loves. Who's the girl that Sugimoto loves and wants to collect the tattoos for?