It kinda makes sense. We got the Cloak & Dagger reference in Wonder Man, and if they're saving Josh Gad from where he is in Door Man in the Dark Dimension/Darkforce, it makes sense for Cloak and Dagger, who've been in the Dark Dimension before, to be able to save Josh Gad.
Not titling this as a theory (I’ll tag it like that cause it doesn’t fit anywhere else) because I don’t have like concrete lore reasons as to why it takes place before, I’m more so giving an opinion saying that it would make more sense to have One Last Kill be set, or even be retconned to have been set, before Frank’s appearance in Daredevil: Born Again Season 1.
I think you could honestly leave the special totally unchanged and just rearrange it’s placement in a watch order and it would honestly flow better. The way Frank just doesn’t even think about the AVTF makes more sense if they just don’t exist yet, he isn’t the sort of character to leave that behind and go into hiding because he got arrested. We don’t know what happened to his base in the Heights that was seen in DD, but we do know that his residence was burned down in One Last Kill, so it makes sense if he just went looking for a new hideout and moved across town from Little Italy to the Heights. He has his whole shaggy not taking care of himself look in this special and keeps it for when he is reunited with Matt Murdock, but shaves it off for his rescue, arrest, and it’s still shaved off for when he’s operating on the same case as Spider-Man in Brand New Day.
It just feels like it makes more sense and flows better as an overall narrative if he’s retired after the nine year gap we last saw from him in Punisher Season 2, then suffers an identity crisis and starts punishing again with the goal of protecting innocents now that his family murder connections are all gone (except for Ma Gunnici as the last one left) and then he has team up with Daredevil, his arrest, and team up with Spider-Man.
This would mean he is doing Punisher stuff to get revenge for his family in DD2 and Punisher 1, works with the FBI and gets to lay low before breaking his cover and returning to punishing in Punisher 2, spends nine years to kill everyone connected to the Castle Family murder and finished his plight as The Punisher, redefines what his role is and finds a reason to continue his life in One Last Kill, and then fights against Fisk’s empire in BA1 before his arrest, to be continued in BND.
The "CYBERTEK SETTLES" front page story in Ben Urich's office is in the Daredevil Born Again Season 2 finale. This is a direct reference to the events of Agents of SHIELD.