As in, for example, the first player starts with 7 coins instead of 5 as written.
That would be all players, not just the first player. Everyone gets their +2 coins at the same time.
How did you learn this? I look all parts of game rules book and cannot see anything about this.
From the rulebook under the "Progress of the Game" section:
Phase 1 - Collecting income
Each player gets 2 deniers from the stock.