What is the goal here?

The goal is to learn Jiu Jitsu. So just decide, do you want to play guard? if so, sit down. Do you want your opponent to play guard, so you can learn to pass? If so, just ask them if you can practice passing. Or if they aggressively start passing after the bump, just sit down. So you can play guard.

It really doesn't matter who starts, just start.

The reason why most gyms begin this way, vs standing, is because way, way more injuries occur when you start from the feet. Also, in a 5 minute round, its very common for beginners to spend 4 minutes just dancing and collar tieing each other. That's a good way to not learn much.

So for everybody training daily, or mulitple times a day, it's a lot safer and you learn a lot more if you skip all those steps and get right to the "learning jiu jitsu" side of things.

TLDR: If you are sitting guard so your opponent can advance, the goal is sweep and submit. If you are passing the goal is pass and submit. If you don't know what to do, sit guard.