I think that would fall under this paragraph from the PHB: "Unless a spell has a perceptible effect, a creature might not know it was targeted by a spell at all. An effect like crackling lightning is obvious, but a more subtle effect, such as an attempt to read a creature's thoughts, typically goes unnoticed, unless a spell says otherwise."
There is some debate over whether having to make a saving throw is enough to tip you off that you were targeted, but hex does not grant a saving throw. You might notice when you have to make an ability check and mysteriously have disadvantage. However, you don't normally roll Perception to detect a stealthy creature--the stealthy creature makes a check against your passive Perception--and of course, by the time you roll initiative, you're starting combat anyway.
It may start initiative, but it certainly does not start combat if the target doesn't even know it was hexed.
This is why I hate, hate, hate "rolling for initiative" being an in-game event that can be manipulated and trigger other events. It leads to all kinds of weird questions over what exactly causes the roll and when you roll again. If I sneak up to an enemy camp, hex the big bad, sneak away, and take a short rest to get my spell slot back before combat (maintaining hex through the rest), is there a new initiative roll when we come back? What if the big bad gets wind of our presence and attacks us while we're resting? Has my hex inoculated the party against "rolls initiative" triggers from the enemy?