You have a list of registered players, and you may have that list divided into teams, although you may want to wait on creating final team rosters and the pairings for the first round of games. Even a registered player may cancel the morning of the event, and you may have a drop-in player you can accommodate and add to the event. So we recommend you wait until your designated start time before you finalize your player list and start with pairings.
Also, on the subject of organizing your players into teams and determining the pairings of players for the first round of games, give yourself at least 15 minutes between the start time of your event and the point when players begin picking table sides and deploying models.
You probably know one of the unwritten rules for first round pairings-try not to match players that just spent hours in the car together driving to the event! Try to give everyone a chance to play someone new, possibly someone they've never played before. The first round is generally randomized, but there's no reason you can't use your discretion to create some dynamic matches. You may consider pairing two players that have similar preferences of style or hobby excellence, especially if they had never met before. The first round of an event is a good way to mix things up a bit and gets players socializing before the stakes for the day get too big.
There are plenty of ways to determine random pairings, but in a team event like Coalescence you want players matched against players from other teams. Divide the players into their respective teams, either on paper or even just by having them stand together in separate groups. Giving colored stickers to players of the same team can help distinguish players from each team, but consider some simple name tags, especially if you're not expecting your usual group of players. Let the players in each team do the work for you-ask them to discuss among their teams to which players fall into specific catergories. Ask them to figure out which one drove the farthest, which player celebrated the most recent birthday, which player has the best painted army from among that team, which one stands the tallest or the shortest. After all the teams have selected members fitting each category (and if someone fits more than one, then ask them to pick one for each category), then you can just use the categories to match players across teams. Pair the tallest players in team green and red, blue and yellow. Then pair the players with the best painted armies in teams green and blue, red and yellow. Etc.
Or you could just give playing cards or slips of numbered paper to each player and have players with matching cards or numbers pair up to play the first round. Be creative! This is a great opportunity for an ice breaking exercise and get your players talking with each other and working as a team.
For subsequent rounds, you don't necessarily need to pair winners against winners and losers against losers, especially for a narrative event. Maybe two players had so much fun in their first game they want to fight a rematch, or maybe there has been some divisiveness in a team which has turned against itself. Trust your instincts as well as your wisdom. Or just make things completely random and trust in the luck of the draw. It's a narrative event, and the best way to create a story is by explaining how a twist of randomness led to an unveiled fate and the fulfillment (or disappointment) of destiny.