I think there's scope for including the scoring as part of the packaging, no "waste paper". My first inclination is a two part sleeve - but I'm assuming then it's a two player game, more players requires some ingenuity - the sleeves start at zero score and cover the lower numbers, moving towards the highest possible score at the centre as the sleeves meet and cover the whole container.

Perhaps a graduated stick, like a long cocktail stick/drink stirrer, for each player, you pull the stick across a line (eg from under the box) to indicate the score. Another way would be to have a stack of counters, like tiddlywinks, you could upsell different counter sets then (half marbles, cut stones, metal, different designs). Counters might work for tie-ins - planets of the Starfleet federation, planets named for houses of GoT or such. Or yes d10's as a sibling comment mentions.

Doesn't mean you couldn't have an app too, but then why not simulate the dice, etc., if you're going to need an app to play the game?