To be a bit more specific, the relevant time interval for this Nature paper is between when dark matter halos began collapsing and when this quasar turned on, not the interval between the start of the Universe until the quasar turned on. However, in the currently-favored cosmology, the "start" of the Universe is followed very rapidly by the onset of structure formation, so the two are effectively the same point in time (at least, for the purposes of supermassive black hole formation and growth). As it relates to this Nature paper, the theory you reference merely separates the "start" of the Universe from the onset of structure formation, so it doesn't affect the relevant time interval for this particular question.
> I always new that there was a relationship between black holes and quasars (In/Out) but was unaware that there was an established relationship between specific events. Does anyone have links to this ?
It isn't so much a link between specific times as a limit on how quickly you can grow a black hole. The formation of supermassive black holes is fairly uncertain[2], but models generally predict that you start with a black hole that is 1–100 times the mass of the Sun and then grow it by accreting gas. There's a limit to how quickly you can accrete gas[3], so there's a limit to how quickly you can grow the black hole. If you put those two things together, there isn't enough time elapsed between the onset of structure formation and this newly discovered quasar was active, with such a high mass black hole.
[0] https://en.wikipedia.org/wiki/Inflation_%28cosmology%29
[1] https://en.wikipedia.org/wiki/Lambda-CDM_model
[2] https://en.wikipedia.org/wiki/Supermassive_black_hole#Format...
[3] https://en.wikipedia.org/wiki/Eddington_luminosity
Edit: modified wording for clarity.