"We are hopeful to have the car in the wind tunnel, which should be at that stage the new car, in June," Stella said in Bahrain.
"The wind tunnel is already commissioned, but there's a process of calibration, installation of the methodologies like the ones you use to measure the pressure, to measure the velocity field, to measure the forces. All this takes some weeks.
"Hardware-wise it exists, the fan goes on. It's really nice for my office because I can hear it. And it's so reassuring [because] we're making progress, but we can't yet put the car model in there for the relevant tests.
"On a new wind tunnel you have to use a reference model in one tunnel and in another to see the correlation and repeatability.
"We don't plan to do it with the new car model, we want to do it with the old car model, understand more about the new wind tunnel and then deploy the new  car."
McLaren's new wind tunnel will not only boost the quality of the team's development work, but it should also help speed it up.
Currently, the team rents Toyota's wind tunnel in Cologne, which involves packing parts into a van and sending it off to Germany.
"When we have a design, we produce the parts for the model, then there's a van that drives to Cologne and we lose a couple of days," Stella explained. "Formula 1 is such a fast business, you can't have this way of operating.
"I don't want to mention the wind tunnel too much because it sounds like an excuse, but it's definitely a deficit in the quality and in the speed of the development because of all these slow operations that you have to do to just get the parts tested in the wind tunnel."
Stella has made it clear that even before the new tunnel comes online, he expects the team to make progress with its current tools and methodologies.
After missing its launch targets with a draggy MCL60, the 2023 opening weekend in Bahrain has shown that for all its deficiencies the team's new car has plenty of development potential.
The first main upgrade scheduled for Baku, which follows a different development avenue that should produce a more efficient car, is still being improved upon, while the team will bring smaller updates to both Saudi Arabia and Australia.
"The wind tunnel alone is not enough to justify the fact that the car is where it is," Stella said.
"We could have done a better job independently of the wind tunnel. Now, this is something we are reviewing. Very honestly, I think this is acknowledged and this has actually given us good learning throughout the group for future developments.
"That's why you see me a little committed in terms of I think we see the car very alive in terms of development."
In Bahrain, Lando Norris and Oscar Piastri qualified 11th and 18th respectively, but neither challenged for points.
Piastri retired from his F1 debut race after 14 laps with an electronic failure, while Norris suffered a pneumatic pressure leak that forced him to pit six times as he finished 17th.