I started in gold2 and reached plat in 2 days (playing crypto with randoms, 4 wins). Plat was still very full of predators then (they started at plat2). Now I generally see just 1-4 predators per game (I assume they all use their dive trails) and I imagine most of them will move on to diamond pretty soon, so platinum games should feel like platinum within a week or two (well there will still be a lot of ex-diamond players in plat after a week, but predators are the ones that make current platinum tough).
Same thing should be happening with gold and ex-diamonds, although I imagine most diamonds have already moved on from gold.
So generally it's hard to answer how long it would take to reach some rank starting now, since that hardly depends on how many games you play per day. The less you play early in the season, the fewer games you should need overall. E.g., it's simply easier to win gold games with just gold players than gold games that contain mostly plat/diamond players.