Most people quest solo. They group for rifts, invasions, and zone events. You can just click on the "Join Public Group" button that appears at the top of your screen for these events. There are occasional quests intended for small groups but they're few and far between.
I have been in a group for about a quarter of all the quests I have done from level 1-45. It makes everything faster (And in Iron Pine Peaks a lot less painful going up and down the mountains alone over and over again.)
And You will be level 6-8 by the time you see your first real zone invasions or rift or events. There is a tutorial zone that gives you your first souls and basic equipment and things.