The target is for 65% of ambulances to reach high priority calls inside eight minutes but that has been missed for most of the last two years.
September's figures are out next week but BBC Wales can reveal a slight improvement up to 58.9%.
Chief executive Tracy Myhill said it needs to satisfy the public.
Speaking to BBC Radio Cymru's Manylu programme, Ms Myhill, who is in an interim role, said targets rightly focused the mind and the emergency target had received a lot of attention.
"There's a huge focus on the one target - but my own view is until we can satisfy people we are continuing to improve that target, it's hard to talk about other things."
Ms Myhill said there were other good things going on towards transforming the service, which include:
"It's a do-able target. It's not an imminent fix, it's a really complex system," said Ms Myhill.
"I can't say to you tomorrow or a next month that 65% target will be hit. What I'm aiming to do is to ensure there is continuous improvement and continuous movement towards that target.
"The whole way this service works, commissions and delivers is different and we need to change with that, to give people the service they deserve," she said.
As for getting rid of the target, Ms Myhill said she was in favour of reviewing it only once it was hit.
"We need to look at this target and we need to make sure it's the right target for the safety, the quality and service for the population but it's hard to do that when you're not meeting it," she said.
"We've got to collectively show improvement before we can change the target to be more meaningful."
September's figure of 58.9% compares to August when just 56.9% of ambulances arrived at the scene within eight minutes.
But it is above the 58.3% figure for July.
Health Minister Mark Drakeford said the August targets times were disappointing, adding that he hoped the new acting ambulance chief along with extra paramedics would be able to make a difference.
There is more on this story on Manylu, BBC Radio Cymru Thursday 23 October, 12:30 BST.
Missed target times for ambulance emergency calls can be turned around but there is "no imminent fix", warns the new head of the service in Wales.