don't worry, I have no blacks either, only lilia/Hina from my 1st 10 premium summons (according to lafate SC use guide), and the rest are event plat/golds. basically right now, just focus on maxing the core units that you have, as well as some of the golds you just got from this gold rush, like bernice, julian, conrad, kerry, fedora.
we have at least a 1 week break for now; getting affection items for your core units will likely be the priority, and you'll eventually be able to get silvers from the next few events as well as fairly decent plat units to use. even full cost plat units with lvl 1 skill can be useful, such as Odette for me (I only got 1 copy of her because I joined late). eventually you'll catch up and do decently well.