A lack of power unit performance was a handicap for the Alpine team last year, when Renault's Viry-Chatillon powertrain division was focussed on a major upgrade for this season, including a move to a split turbine and compressor arrangement for the first time.
Szafnauer says that his colleagues have done a "brilliant job" in closing the gap.
"We think we've made a step on the power unit," he said. "And we're within probably 10bhp of the best, and somewhere in the middle.
"I think Viry have done a brilliant job. And it's up to us now to keep developing the car."
The significance of the Renault's strong early season form is that a development freeze is in place until the end of 2025, with some power unit elements already frozen as of last month, and others to be signed off in September.
Szafnauer noted: "So that allows us to work closer with our power unit team to make some improvements that we might be able to make with architecture changes on the chassis.
"Some other things that are still free to us. But also to now focus with what we have to also improve on the chassis for the future."
While performance has improved Alpine suffered some engine issues in the early races.
The engine that Fernando Alonso ran in Bahrain was sent back to Viry but has since been passed fit to return to his pool.
However, he has lost the V6 he used in Saudi Arabia after a water pump failure led to overheating and his retirement from the race.
"It was just a precautionary change for us to test some things on the dyno, and it tested okay," said Szafnauer of the Bahrain unit.
"So that engine will be used again. The other one unfortunately, where the water pump, although the water pump isn't part of the ICE, you can change it, but it overheated the ICE, so that one is gone. But we'll be okay."
Alonso crashed in Melbourne qualifying after an oil pressure drop triggered a fail-safe mode that shut down his engine mid-corner, but that engine has also survived and was used in the race.
"It was O-ring on an oil seal," said Szafnauer. "The O-ring fretted, the oil leaked out. We have a fail-safe mode to try to save the engine, so when you see a drop in oil pressure, the fail-safe mode kicked in. And that's what happened. So the fix was an O-ring change."
Szafnauer says there are no concerns about Esteban Ocon's Melbourne engine, despite radio messages urging the Frenchman to cool it down during the race.
"That because you're in a DRS train. Had he been up front, he wouldn't have needed to do that.
"If you plan for the DRS train, and have your cooling package that way, you add too much drag.
"So the right thing to do is be competitive, when that happens lift and coast or move out. But you've got to tell him, he doesn't know."
