There's been plot happening for months now, dude. Years, if you consider the leadup. If you're referring to plot in the sense of official storylines, quests and areas one can visit to engage in battles vs raid boss like in most MMO? Nooot~ so much. Don't think ED goes in for that gameplay style, overall.
That said you're perfectly able to join in and be one of the many CMDR chipping in the humanitarian crisis of Thargoid attacks on space station, going off to them and ferrying folk away from the burning wrecks (or bringing supplies to repair 'em). There's also going out and fighting Thargoid, in specific sections of the galaxy, although you'll need specific weapons, scanners and in all honesty a Wing of fellow CMDR if you hope to survive a battle; winning solo is very tricky to achieve.
So like always its walled off behind ridiculous grinding for faction