Is there a universally accepted idea of how old Natasha was when Budapest happened?
I haven't found one, and I can't parse one out.
I was hoping an answer might show up on commentary but the blu-ray doesn't have commentary. So I assume that if we get that information, it will be in the Art of the Movie book, which BN.com indicates comes out in August of 2022.
That said, here is some pointless and unfounded math:
Natasha's ID in the openings give her a birthday of December 3, 1983. Accepting that as accurate for now (which means believing SHIELD had the wrong birthday for her, which is... hilarious and great, tbh), and assuming release dates of non-flashback-movies are accurate in-universe, that means she was 26 in Iron Man 2. Budapest was Nat proving her loyalty to SHIELD; by IM2 she's seen as loyal enough that she's in Fury's inner circle.
Coming at it in the other direction, while we don't have a date for her Red Room "graduation," the opening credits do give us more of a sense of Nat aging. We know how she looks at eleven (like Ever Anderson); we see teen Widows who look very clearly younger than Nat did in the Ultron flashbacks, when she was getting her hysterectomy.
(Two things I should note here: I assume the red-haired girl with a gun in the BW credits is Nat, but we don't actually know that; for the sake of argument, it could just be a different Widow. And due to Wanda's magic, it's very possible that Scarlett-As-Nat is how Natasha remembers herself but she actually looks like Ever Anderson or the red-haired girl in the credits.)
From a different angle: Young Antonia was played by Ryan Kiera Armstrong, who was born in 2010, so when it filmed she was presumably about 9 or 10, so say Toni was that age. But then we'd need to math to get to adult Antonia, who is played by Olga Kurylenko, who was born in 1979, which means she would have been about 40 when it filmed, which is older than Scarlett when we know that Nat was much older than Antonia, so that helps us literally not at all. But for math purposes, it's important to note.
Also, I know nothing about costuming, but I didn't notice anything in the Budapest outfits that help us place it in a specific year.
We also know that the timeline is murky, because- again, if we accept all on-screen film canon as equally accurate canon- Nat says in Avengers she was making a name for herself as a mercenary before Clint was sent to kill her and saved her instead, but in Black Widow she says that killing Dreykov was her final act of separating from the Red Room. Nat's loyalty to SHIELD would be less suspicious the farther out she is from defecting, but we don't know if that's measured from when she first left the Red Room or when she tried to take out Dreykov.
(Full context here is also important because we know that after Nat's defection is when Dreykov started using Melina's techniques on the other Widows; I had been assuming that was right at Budapest, and Toni was the first attempt, but could it possibly have been earlier and Toni only got the implant after Dreykov decided her disfigured body was fundamentally broken? There's no good answer here but there are a LOT of intriguingly bad ones.)
So IF we accept all of those givens, which I am not fully ready to do but for the sake of argument will do anyway, I think Budapest had to happen sometime between 2002 and 2009, and I think I would place it around 2007, but I am not particularly confident in that assessment and am quite happy to be proven wrong.
