I started this the last week of September 2019, so at the end of December I was L13. I progress one level every 7-8 days. I use the site when I wake up, maybe around lunch time, and then at night before bed.
I 99% use the mobile site since I don’t use a computer outside of my day job - so I don’t have access to scripts, which is okay.
Compare to my friend who started the same time I did, I think he’s level 5 or 6 right now. He tends to make a lot of mistakes on the kanji which slows his progression, and he doesn’t follow a strict schedule, so he might delay reviews for a half day or so from when they appear.
So a realistic 3 month goal is probably somewhere in between L6 and L15.