What factors influence in the first games to enter in a League?
Here's what I know, I'm sorry if it's not a complete answer.
In 5v5, everyone's elo is important, because Riot will match you against a team with similar elo. This is important because it's not just winning that matters, but who you win against.
For instance, if you win 5 games against 5 Bronze III teams you'll be placed into Bronze III-II. But if you win 3 games against Gold 3 and lose twice against Platinum or Gold I, you'll likely be placed into gold.
In short, it's not just the quantity, but the quality of wins that matters.