So in my current campaign, we are 12 sessions in and 3 of those featured no combats making it 25% exactly. 2 of those were fun downtime sessions after quests, and 1 was a night of burglary that could have turned into combat but was avoided. I think the next session is likely to be no combat too as they are about to advance to the next tier of play and leave the starting town which I’m finding is taking more time to set up.
My campaign consists of 3 hour long sessions played over video chat. I find if there are 2 combat encounters in a session that generally takes up the entire session and can see some players find it a bit relentless, so sessions that are non-stop combat are about as common as those with zero combat, and usually come back to back. (Session 11 was non-stop combat on the way back from the first big dungeon, so Session 12, was zero to act as a palette cleanser).
I put quite a bit of thought into the pacing and rhythm of the campaign, and will sometimes remove encounters when it is becoming a slog, or add them in when events needs spicing up.
I definitely think the first session of every campaign should have some combat though, starting off things with a bang and letting the players get a feel for their characters.