I think you overrate time. I think it is better to build big at once and early. Spreading the volume out does not promote size growth only cash flow as you get the building in before the next game.
It is better to go big. Also, I don't think its been noted much but pricing should be lower as you expand. I don't know who came up with the guide for arenas but i think its pretty terrible.
A good guide for expanding: Charge 0-10% below max capacity as you will expand during the building. You will want to sell out your games. Then as you expand beyond sell-out, your earnings will pick up the new arena space.
The idea is to reduce price but not by too much. It is better to worry about expanding your arena than undercharging.
Lastly money is mostly made via trading players. Your players should be assets. If they are not, sell them.
Two types of assets:
1) Long-term = your starting 5 that wins games+divisions.
2) Short term = your trainees.
In low divisions they can be 1+2. That means you should have plenty of cash to expand your arena.