I just began watching Suisei no Garugantia and didn't understand why there is that unexplained (at least so far) war against the Hideauze aliens. Who attacked first, and for what reason?
If you just began watching the series, this answer will be a huge spoiler for you. The information here is from episode 9, so I'd advise you to wait for the episode before reading this.
In episode 9, Ledo got hold of some information from the past in which he learnt about the origins of both the Hideauze and the war between them and mankind.
Spoilers from episode 9 from here onward!
Before Earth's fifth ice age, a group of humans underwent heavy genetic modifications, in order to adapt themselves to space environment, so that they could migrate from Earth. These people were called the Evolvers. The human Evolvers are what became the Hideauze.
There were countries that stood by the Evolvers, and countries that stood against them (the Continental Union). The opposition movement against the Evolvers opened fire against them. From there things escalated into a war between "regular" humans and Hideauze (genetically modified humans), because they both wanted to flee from Earth (using a portal being built by the Continental Union), and saw each other as a threat.
Basically, "regular" humans attacked first, because they saw the genetic modifications the Evolvers underwent as a sort of blasphemy (and were, most likely, afraid of them). However, the war only got to what it is now because the Hideauze saw the portal being built as a threat to them (because they'd be stranded on Earth), and decided to take preemptive action against "regular" humans.