After a frustrating run with just one point in eight weekends, the team made a significant step in Qatar, where Valtteri Bottas claimed eighth and Zhou Guanyu ninth.
The six points moved Alfa up to eighth place in the championship table, ahead of Haas, leaving it just seven points behind Williams.
While Williams has made it clear that it has switched its focus to the 2024 project its rivals Alfa and AlphaTauri have continued to bring new parts to the track.
Haas is putting a lot of faith in a major upgrade package that will be unveiled in Austin this weekend, adding an extra dimension to the battle for the minor placings.
“We are convinced that we can fight for P7 until the end of the season, based on our decision to keep developing the car,” Alunni Bravi told Autosport.
“But of course, we need to execute each race weekend a perfect race like Qatar, both from the team side and the driver side.
“Qatar was a good reward, it's been good for the team, for the confidence and for our drivers, after a tough period.
“But the championship is still long, five races with two other sprint sessions. So still room for improvement. We need to look ahead of us to find extra performance in the next race.”
While the Haas upgrades have attracted more attention due to their comprehensive nature Alfa has quietly been changing its car race-by-race, with a revised beam wing in Qatar serving as a finishing touch to the recent run of updates.
"There is not only one way to develop the car, it depends also on what you find in the wind tunnel,” said Alunni Bravi.
“I think that every team has some developments, but then you need to understand if there is anything that brings that extra performance that is necessary to do the step.
“We decided at the beginning of the year to really push with the development, and we will keep developing the car until the very last race. Sometimes you can have a major upgrade, like we had in Singapore for instance, with the new floor.
“But then after a big upgrade, we always try to optimise the package. In Qatar also we completed the package introduced in Singapore with a lower rear wing flap that was necessary to have a good performance on the medium/low-speed corners, but not to be penalised too much with the top speed that still remains one of our weakness points."
Alunni Bravi believes that the car will be competitive in Austin, but he sees opportunities to score elsewhere as well.
"I think that for us we have seen that where we have a low-efficiency track and we need to have a higher downforce level, our car suits better these conditions,” he said. “So we think that Austin will be in our favour.
“Mexico will be a bit more difficult because I think there, Williams and AlphaTauri will be really strong. And then, of course, Sao Paulo and Abu Dhabi, we have always seen really interesting, races and a bit unpredictable.
“Las Vegas is new for everybody. We don't know what we can expect. But at Miami our package was competitive.
“I think what will be important will be the mindset, the approach of the team and the drivers, what we will find with the new upgrades, and of course, we need to have both drivers driving a solid and flawless race, because each point will count at the end of the season. And we don't need to make any mistakes on track.”