There's only one "intake" each year, if you get it, you start your job in October that year.
This means that, yeah, companies start talking to potential foreigners whom they want to hire in say late last year, register them to the system by March. And by the end of March, the government would announce the winner of the lottery. Yes, the number of applicants is much larger than the quota, so every year about 1/3 or 1/4 of the applicants would actually "win the #H1B lottery" (3/12)