I stopped keeping up with current events in hip hop in like 2018, give or take a year. So I'm not really up on this like that but I'd say he definitively became the biggest rapper when he succeeded the throne from Wayne...
Wayne was still the biggest name in hip hop when he dropped Carter IV in 2011. Drake also dropped Take Care that year but I think Carter IV was more anticipated, Wayne still had the edge...
Drake didn't drop in '12 and that saw Kendrick really rise to superstardom with Good Kid, Maad City. 2012 was more of a transition year that saw OGs like Wayne, Kanye, Hov start phasing out for that Drake, Future, Dot, Cole, Meek, Wale, Nicki class...
So I don't think anyone had 2012, Drake was the biggest name, but he hadn't firmly taken the reins yet...
2013 I vividly remember cats calling Nothing Was The Same a disappointment, both Meek and Cole had better drops in real time. It's funny how Nothing Was The Same has become better received in retrospect because cats were not really feeling it in real time. Now he was Drake, his momentum didn't take a hit as much as the public perception of his artistry, and he has a massive white and nonblack following, international, so he was still ascending...
But these years in the middle of the 10s you could easily argue Future or Kendrick were bigger...
He didn't drop for a year and a half or in the '14 calendar year, which was really a weak year for hip hop. He built massive anticipation and when he dropped If You're Reading This It's Too Late, he delivered on the anticipation and it set the tone for an amazing 2015 in hip hop, a grip of classics dropped in '15...
He dropped two, because What A Time To Be Alive also dropped in '15, and '15 was honestly the beginning of the more aggressive, matured flow Drake...
So if you gotta hold me to a year, I'd say 2015 is when he definitively took the throne. And that's the thing, you can't even say he had the best music that year. Krit, Dot, Future and others all dropped classics in 2015, but Drake, already the biggest brand, finally delivering on massive anticipation from an artistic viewpoint, that was the year...
So it's been 8 years, by my count...