Right. As Darin says, because the minor train limit is 2, a minor could decline to upgrade their L to a 2 (after acquiring 80 in their treasury) and instead buy a 2 as a second train for 120 once they have 120 in their treasury. I have done this before, but the 2s were broken by another company before I bought mine.
The game is in phase 1 until a 2 train is purchased or an L train is converted to a 2 train.
The game is in phase 2 from then until a 3 train is purchased etc.
The phase summary table on Page 5 clearly states that phase 2 starts when an L is converted OR when a 2 is purchased outright.
Some of the high paying minors, if floated early, can indeed afford to buy a 2 outright, having declined to upgrade their L to a 2. They will then be in the glorious position of running a 2 and an L for loads of money. In my experience, this is not uncommon.
There is nothing in the rules preventing the first active 2 train in the game to be purchased outright in this manner, rather than arrive as a converted L train.