Ingham has been selected for the All Whites alongside 17-year-old brother Dane, with the Australian-born pair able to represent New Zealand through their mother.
"It's huge, not just for me and him but for our whole family," Jai said following his first day in All Whites camp.
"It was amazing to get the call-up with Dane and if we can both get on the field at the same time, then I'm sure we'll show what we're made of."
After speaking to All Whites head coach Anthony Hudson, Jai said choosing New Zealand was an easy choice for the Ingham brothers.
"I talked to Anthony and he was very positive, he has a vision of what he wants to do here with New Zealand football and it's a very good thing to see," Jai said.
"Even coming straight into the camp, I've seen how positive it is and how much everyone wants to win here.
"All the information they feed us is winning-related and that's what we want to do."
Joining Ingham in All Whites camp is Victory teammate Marco Rojas, who has been in outstanding form this season.
"He's a really good player and I know exactly what he's about," Ingham said of Rojas.
"It's good to get amongst not just him but all the other players that are coming back from overseas. Being able to learn off players like that is going to be an unbelievable experience."
Hudson is just as excited to have Ingham on board as the All Whites look to qualify for the FIFA World Cup for the first time since 2010.
"He looked really bright this morning and it's great to have him in the camp,” Hudson said.
"He's a really, really exciting player – he has loads of energy, is really attack-minded and you can see this morning just from one session that he's someone who is really going to add to the group.
"We’re really pleased he's here."