I think reaching 1400 elo after a year of decent study after learning the rules is not too unreasonable. To reach 1400 in a year you would need to be either talented or hard-working. Climbing the elo ladder does get much harder though, as you mentioned. To reach 2000 in two years you would need to be both hard-working and talented. To reach 2850 in a lifetime you have to be hard-working, talented, and a particular Norwegian GM.

In which format? I highly doubt that someone could do that in bullet unless they played full time.

Bullet players are already on average a higher percentile of chess players so the elo is skewed

It's generally thought that beginners improve most quickly by playing slower chess (e.g. 15+10 or even 30+20). If you're a 1000 and you only play bullet, you may end up cementing some of your bad habits. Whereas with slower time controls, one has time to calculate some deeper lines and really try to understand the position. And if one spends a year getting to 1400 in rapid, one will find that one's gains from slower time controls will quickly bare fruit in the lower time controls (once you learn time management).

Generally speaking, players playing bullet are more interested in having fun and less interested in gaining elo (which of course is totally fine).

As with all things, it depends on how intense you are. I've seen a guy go from 900 to 2k in 6 months, but he played over 1k hours during that time (yeah). It really depends on how much you are willing to play!

Edit: Just to be clear, I'm talking about online rating

I don't know about Elo but I reached 2100 from 900 Glick2 (the rating system Lichess uses) on Rapid in little over a year.

I started from beginner to about 1800 on lichess in about a year of casual play and watching some grandmasters on youtube. I am 30 years old, i think younger kids can do better and we know many prodigies do.

I guess this is different to official rankings and/or elo though, so that was my mistake.