In the very early game, portal cooldown is one of the most limiting things in the game. Seeing an 8h or 4h cooldown can be quite daunting and make you think it's time to stop playing for the day. Going to an undesired dimension can also feel bad.
Consider adding a small incremental cooldown reduction available very early in the game. This upgrade doesn't actually have to be significantly impactful on the cooldown, it just needs to give you the feeling you have some influence/control over it. But making it a significant reduction and increasing the base portal cooldown a bit could also work.
E.g. some cheap ascension upgrade that reduces portal cooldown by 1% every time you take a portal. Would make thematic sense. Adding it for 100-200 SP after the special box magnet or portal traveler upgrades might be a good spot.
But it could be a random chance from killing enemies/giants too, or something that sometimes replaces a coin or similar to the chest hunt key, or something else that is more consistent/easier to balance.
I wouldn't add it as a random box reward, as that would feel bad for people later in the game who have a 1h cooldown.
I would also make it a percentage instead of fixed amount of minutes so it can be decent in the early game without becoming too strong with more portal upgrades.
