On the first day of basic indoctrination, pilots bid for their aircraft and base. The 737 was my first choice and luckily I had the seniority in class to hold it. Every class “drop” has different options. For the the most part, there has been about 30 737 bids, 6-8 A320, 10 757/767, 2-3 777 or 787.
As for the timeline, I started ATP in Jan 2019. Feel free to check out the link for more details: