Er... actually I think a better way to go would be to make assassins with high EARLY bases, but low base growth and high scalings. Assassins need to be able to... well... be assassins. Starting assassins with no or poor damage means they can't really do their jobs and fighter-types will be used instead. That means enjoy the league of bruisers.
Instead, if we give them strong early damage but incredibly low growth on those bases, they'll HAVE to build damage items to keep up as assassins. If they don't build damage, they're just gonna be mobile fighters with no real CC. We also need to keep % damage the heck off of assassins. % damage is for tanks and sustained damage types and it's what makes the dreaded "damage bruiser" like Ekko viable.
If we tweak assassins like this, they will be able to get kills early if they play well... but if you can PREVENT them from doing so, they will be pretty crap. Feast or famine play is FINE for a role like assassins. If you pick an assassin over a "safer" pick, you had better be able to assassinate people! If you fail to do so, you shouldn't be good for much else than being a half-assed splitpusher or something. It's the tradeoff they need for being able to 100-0 a target who is safely behind is own lines and then escape to safety. Otherwise, that shit is just broken.