The team was only eighth fastest overall in Spain, having lost most of the final day after a hydraulic leak led to a fire.
Like other teams, Alpine has brought a package of updates to the Bahrain test.
The car didn't set any headline-grabbing times on Thursday when an issue restricted mileage, but on Friday Esteban Ocon was fastest in the morning session.
"Obviously we had a strange day yesterday," said Alonso. "And we had some issues that we attacked in the afternoon, especially when I jumped in. So not the laps that we wanted.
"But yeah, we made some progress. The car felt better than Barcelona for sure. We brought some new things here and more to come in the next days, and hopefully into the race one.
"Everyone is working flat out. And I'm happy, I'm optimistic that we will be much better in the next couple of days, and especially in race one."
Alonso said that Bahrain hadn't highlighted any particular problems with the A522, and in fact the team learned that it behaved well in the much hotter conditions.
"I think we had a good surprise on that respect. I think the car is working well on high temperatures. We didn't have any issues on all the cooling systems and brakes, and all the characteristics that Bahrain has different compared to Barcelona.
"So everything was running okay. And I think as I said we are more optimistic than maybe one week ago."
Alonso expects the 2022 formbook to change as the season goes on.
"I think it is going to be a long game, that is for sure. The rate of development is going to be huge, and there are 22 races. I remember here last year I retired the car and Esteban was P12 or P13, so zero points after Bahrain.
"And then we won a race in Hungary, and we were enjoying the season from then on, so I think this year is going to be a long game to play, and I am confident that we will have a good season."
Asked if the team can rise above the midfield he said: "It is an interesting question, and we don't have any answers yet, I think we have to wait and see to understand how the first races develop and see what we need from the car and from the package.
"I am optimistic that the team is putting a huge effort into this programme, and we have the support from our president, and we have the support from everyone at Renault and Alpine, who came to F1 last year with an eye on this set of regulations to try to be a contender in the future.
"If that future will be 2022 or 2025 I have no idea, but there is this commitment and this view which I share and I embrace, that is for sure."
Alonso insisted that the team can challenge for titles.
"We think that we can have a chance," he said. "With a new set of regulations that started this year, in a short/medium term programme Alpine should be capable of fighting for the championship.
"And that's why we are here and why we work so hard. There is the budget cap in place, there are other things that F1 went into. And I think there is a possibility for everyone, and that is why Alpine and Groupe Renault in general are here."