The heavily revised new W15 was launched at Silverstone on Wednesday morning, ahead of some initial shakedown laps by Lewis Hamilton and George Russell.
Wolff is optimistic about the prospects for the new car, citing a "buzz" in the Mercedes camp, but he acknowledged that it won't be easy to take on the team that has dominated the last two seasons.
"On one hand, you need to be realistic about the odds of beating a team that is a fair chunk ahead under these regulations, and who got things right over the last two seasons whilst we have not," he said.
"There are no miracles in the sport. On the other hand, our ambition is strong. It is Red Bull and a very successful car that are the benchmark we are aiming to beat.
"I do not know when that will happen, we do not have any crystal ball. But we will know soon enough how far ahead they are and the task in front of us."
Wolff made it clear that the team's performance over the first two seasons of the ground effect era has not been good enough.
"We got it wrong with the new regulations," he said. "But when we will be looking back in 10 years, or longer, and you're going to read that we finished first eight times in a row, and then third, and second in the constructors', it will look like it was a respectable result and wasn't so bad.
"But this is not counting another team and another driver winning most of the races.
"So our aim is to consolidate our positions towards Ferrari and McLaren sometimes Aston Martin, and be at the forward part of that group.
"At the same time, trying to race at the very front. This is our aim, we're determined to do so. And at the same time, we know how difficult it is, because you're a step behind your main competitor that has got it right straight from the get-go.
"But we love the challenge. And this is why I'm so eager, and all of us are so eager, to see the car finally driving."
Wolff says that the disappointing form of the W13 and W14 obliged the team to take a look at what needed to be changed in all areas, and especially why they didn't perform on track in the manner that the data suggested.
"I think the most important thing is that you look inwards," he said. "What is it that we got wrong? Why did the virtual world not correlate with the real world? And I think we found some clues, we went in this direction, we tried to eliminate as many as possible variables.
"And the buzz that is in the company is something that I haven't seen for so many years. We know it's difficult, we know it's a big mountain to climb because if a team is far ahead like the Red Bull was last year, that's not easy.
"But we have a superb driver combination, hopefully a fast car, the best people in the factory that are giving it all in order to succeed. And I think there's some very good ingredients to be back in the front again."
