I do not know. Roster and coaching talent are not enough to compete for and/or win championships. Luck is another factor, but the necessary sphere all three must live within cannot be dismissed as trivial.
For this reason, I do not believe the entire Super Bowl era can be evaluated in regards to Dallas' chances. Instead, it would be more prudent assessing the NFC East's win/loss records and winning percentages since Jimmy Johnson's influence evaporated.
Since then, Dallas has occasionally fielded genuine roster talent. Or has sometimes employed solid coaching talent. Or briefly and simultaneously enjoyed both. Certainly, bad luck has reared its ugly head from time-to-time along the way, but the environment--the culture itself--has been a literal shroud hanging over the franchise since before Super Bowl XXX.
Let's look at this from a slightly different but similar perspective. The NFC East since the 1997 season:
Giants: 2-1
Eagles: 2-2
Washington: n/a
Cowboys: n/a
Giants: .667
Eagles: .500
Washington: n/a
Cowboys: n/a
Here is an observation related to culture change. Washington flopped to 4-13 in the 2023 season. Almost did a repeat last season finishing 5-12. Yet, sandwiched in-between those lackluster seasons in the post-Daniel Snyder era was a 2024 postseason appearance in the NFC Championship Game.
That small blip may flatline from today forward, but it did happen. For the Cowboys? Since Johnson's Cowboys faded away? No blip has happened.
So, my answer to the thread question 'Can we be one of those teams by 2027?' is another question.
Will Jerry Jones and Stephen Jones (the architects of this franchise's culture since the good old days ended) continue overseeing the franchise's front office through Super Bowl LXII?
If that answer is yes, my answer is, "I don't think so." If a shakeup happens within that duo or something miraculous occurs that subtracts both men from the picture between now and then, my answer is, "What the heck? Why not?"