The Boost Mobile-backed driver had arguably the best weekend of his career to date, scoring his first pole position that he converted into second at the Sydney SuperNight.
With that, the second-year full-timer has slotted into fourth in the drivers' championship.
Kostecki led much of Race 2 at Sydney Motorsport Park, only to be usurped late in the piece by Mostert who went on to win the 77-lap affair.
“To get pole and get that monkey off my back is pretty cool,” Kostecki told Speedcafe.com.
“We sort of had a few hurdles, the Safety Cars weren't in our favour, but pretty confident that if the race had played out and stayed green we probably would have run away with it.
“A big credit to the whole team. From where we started last year to where we are this year is just a complete overhaul. We're a small team compared to the others and we're punching well above our weight.
“I'm sick of hunting, I just want to be the hunted. I was definitely the hunted for the majority of that race, but Chaz did an awesome job there getting by us on the super soft and when he put the wets on he did the Chaz thing.”
Just 30 points off the lead, Kostecki sees no reason why he can't be regularly among the front-runners.
While Mostert is currently the man to beat, Kostecki believes van Gisbergen will be his biggest opposition.
“We're right on that bubble inside that top three there,” said Kostecki.
“Shane is going to be bloody tough to beat this year, but we're not going to show up here without fighting.
“I've got an awesome team around me. Everyone is really passionate here at Erebus.
“It feels great to have Betty and Daniel [Klimenko] in the garage as well as all our partners.
“Barry [Ryan] has put in a lot of effort to make the garage look pretty cool and the whole outfit looks fantastic.
“We just want to show everyone that we're not here to stuff around and we're here to stay.”
There is, however, still one box to tick for Kostecki.
The 24-year-old is yet to win a race, though the second race of the season showed that's probably not far away.
“It's been close now a few times,” he said.
“But it's just awesome. It's been three or four events in a row where we've just been up in that top three, top five, pretty comfortably.
“We've just been missing that tiny little bit. I think we found a little bit overnight and went a completely different direction in the race and it worked out well.”
Kostecki's season continues across March 26-27 at Symmons Plains International Raceway.