Does having green boogers all of a sudden with no clear runny nose beforehand indicate a sinus infection?

No: Oftentimes, nasal mucus dries up in the nose and present with a yellowish or greenish color. Still, even if it's thick mucus, it does not suggest a sinus infection without other painful symptoms. You can get same thick mucus when you have early stage cold..

Not always: You can technically go directly to a sinus infection, without having clear drainage first. Without getting a culture from your sinuses, it can be challenging to diagnose a sinus infection. Some studies say that you need at least two symptoms to more convincingly diagnose this: green/yellow (purulent) drainage, facial pressure or pain, congestion.