In China, Sergio Perez achieved the team's best result of the season so far as he rose from 12th on the grid to earn eighth place on merit, beaten in the midfield battle only by Daniel Ricciardo's Renault.
However, Green says that while the team maximised its potential in Shanghai, real progress will be seen after the Spanish GP.
The development of the 2019 launch car was compromised by last summer's financial squeeze, but now the influx of finance from new owner Lawrence Stroll will start to pay dividends as new parts come through the system on a regular basis.
"The updates that we've put on, we're getting closer to optimising them," Green told Motorsport.com. "The Bahrain test helped us a lot to understand where the sweet spot of the car is.
"Baku has always been strong for us, and hopefully it will be strong again this year. We'll just have a Baku specific downforce kit. And then we've got updates coming thick and fast after that.
"Spain is where things start to happen. We're still a long way off where we want to be, that's for sure, and it takes time to build the team up to challenge where we want to be challenging, while other teams have made big steps. We've been cash-strapped for many years. It's going to take time to build up the team and move it forward. We've just got to be patient."
Perez drove a perfect race in China, moving up from 12th to eighth on the first lap and taking full advantage of the fact that from outside the top 10 he could start on the medium tyre, while those he jumped were committed to softs.
"Eleventh and 12th on our numbers was always better than ninth and 10th, as far as qualifying positions were concerned," said Green. "So we were happy with 12th on the grid. You're never going to beat the top six.
"It was a strong race by Checo. It was a difficult one-stop, it had to be driven really precisely, and he did it. There wasn't a lot of margin in the tyres to pull off a one-stop. He had a really good first lap, he knew it was a track position race with a one-stop. The track probably came to us a little bit to us."
Perez's teammate Lance Stroll rose from 16th to 12th by the flag, passing Kevin Magnussen on the last lap. The Canadian has yet to make it out of Q1 this year, but Green says that his potential is clear.
"He's been really unlucky. He was unlucky in Australia, he was blocked in qualifying. I think with hindsight we would probably have done the strategy slightly differently [in Shanghai], because he had another great start. But we didn't really know what would have happened if we'd gone the other way. But I think he deserved to score a point.
"The potential is there, and it will come through. We always said it's going to take half a season for him to settle into the team and for us to understand his need and for him to understand how we work.
"We're still in that process, it's not something that's going to happen overnight. We see it all the time with drivers coming into a new team, it takes some tome to adapt, and he's exactly the same. But he'll get there."