I empathise, having been through the exact same scenario on and off for a few days now (carrying a team of randoms as well). That said, I did eventually start winning some blueprints. R. N. Jesus will smile upon you soon.
Making friends and forming a squad is a good way to maximise the chances of winning the blueprint you want. It's more frustrating when the same blueprint drops over and over (or none at all), and when the one you want does eventually drop, a random player wins it, repeatedly. Prologue is the worst in this regard because it has the highest number of fresh players who wouldn't have the blueprints. Alien Myths is a bit better.
Try adding some friends though, it improves most aspects of the game, loot included. That said, I play mostly solo as well, so I hope my suggestion doesn't invalidate my advice for you. It costs nothing to add some friends.