Minions don't spawn until 1:30 into the game, but it's entirely possible to win or lose before anyone has farmed a single minion. The majority of players in the pro scene have found out just how important level 1 strategies are due to the LCS, and even now have to formulate multiple plans so they don't get predictable in what they do. Level 1 matters, which is what made it such a gigantic deal when CJ Entus Frost's then ADC Woong looked a the screen during a pause against TSM.
A good level 1 can turn an inherently losing match-up into a winning one, or snowball an even / counter match-up even harder than normal. Kills are the best outcome involved, but seemingly small things like opponents buffs or denying the enemy duo lane double golems can lead to winning lanes. We all know how important vision is on Summoner's Rift, and it's as true at 40 minutes as it is as 2 minutes. Even in solo queue, you do your team no favors by waiting in base for that 4th health potion or sitting by your tower while you wait for the minion wave.
Certain teams are going to be better at fighting level 1 due to their skill sets. Having a Blitzcrank, Alistar, or Thresh is almost reason enough to want to brawl at level one. The key is forcing something, anything to be done at level 1. Acing a team level 1 will almost certainly obviously win you most games where it happens, but even getting early flashes out of opponents can swing entire lanes in your favor. If your team has heavy level 1 cc, it is in your best interest to look for a fight.