Tony Gonzalez pushed back retirement because he believed the Falcons can win a Super Bowl. Steven Jackson and Osi Umenyiora migrated here because they believed the Falcons can win a Super Bowl.

Ray Edwards? His mind was on things other than a Super Bowl — maybe an underwear ad or a club fight in North Dakota. Gone.

So let’s start with this: If anybody characterizes the 2013 NFL season as Super Bowl-or-bust for the Falcons, it’s fair. Winning the division, making the playoffs, winning a postseason game — none of those achievements represents how the franchise will measure success, nor should it.

But the Falcons still have too much to prove to assume anything. This goes beyond the fact that the defense still needs another pass rusher to pair with Umenyiora, as well as a starting cornerback (or two), and maybe a linebacker. There’s still the draft. There’s still some shopping to be done at the Value City, street-free-agency discount table.

What ultimately will make the Falcons a championship team or not is something we can’t possibly know yet.

Umenyiora, who played on two Super Bowl teams in New York, called the present-day Falcons “the most talented team I’ve seen in my life, probably.”

Which translates to what, exactly?

“Talent is just paper,” he said. “I’ve seen plenty of talented teams get punched in the mouth. I’ve been on the receiving end of that, and I’ve also been on the giving end. It’s all how well we come together as a team, and that will determine whether we win or not.”

The Falcons took a step last season: They won a playoff game, but the enduring images are second-half collapses against Seattle and San Francisco. The defense had no pass rush, poor tackling and a seeming aversion to covering the tight end. Matt Ryan and the offense couldn’t mount even a field-goal drive against the 49ers in the second half.

Talent suggests the Falcons will be in the Super Bowl conversation again. But San Francisco has talent. Seattle had talent even before adding Percy Harvin and Cliff Avril.

Former NFL general manager Charley Casserly said, “Both of those teams are better.”

Casserly likes the moves made by general manager Thomas Dimitroff and presumes the cornerback situation will be addressed in the draft. But when asked what ultimately will make the difference for this team, he said: “Probably Matt Ryan.”

The window for a title seemingly has never been this wide open for the Falcons. They can’t assume they will have Gonzalez back in 2014, and they can’t assume Umenyiora and Jackson, highly motivated veterans with something to prove, will have the same mindset (or health) in two years.

But Casserly brought the conversation back to Ryan.

“I think the Falcons’ window (for a title) depends on the quarterback and some of the talent around him,” he said. “Matt Ryan is really good. I’m not saying he’s Tom Brady or Peyton Manning, but you never see the Patriots’ window close because they have Brady, and you never see the window close with Manning.”

Umenyiora for John Abraham is an upgrade. Umenyiora’s sack totals dropped the past two seasons — from 11 1/2 to 9 to 6 — but that can be explained in part by reduced playing time and sharing duties with Jason Pierre-Paul and Justin Tuck.

Umenyiora laughed when asked if the reduced playing time affected him emotionally, then said, “To say that it was ideal for me — it wasn’t.

“Obviously I wasn’t able to play as much as I would like, but I think that set me up for the situation here. I have a lot less wear and tear on my body than I would have if I had played all of those downs. So the disappointment is a blessing.”

Casserly echoed that sentiment: “I watched a lot of games in New York. Osi had some good games, but overall many believe he had an off year. He’ll be motivated. With Abe, you don’t know what you were going to get next year. He might give you sacks, but he might not give you a lot of plays.”

The Falcons lost to the Giants in the playoffs two years ago. Umenyiora said he couldn’t evaluate the Falcons that day, he only knew that New York “had been through that before. We had gone through war in the playoffs two years earlier. It just takes time.”

The names on the paper indicate it could be the Falcons’ time. But to borrow Umenyiora’s words, the telling point will come after they get punched.