But if particles have trajectories, I should be able to precisely predict where they are at any time, but that's not the case. I cannot observe the Bohmian trajectories in, e.g. the notorious double-slit experiment. All observable I get are probability distributions, which can be observed with ensembles of particles. The Bohmian trajectories are just a fiction to claim some determinism which is not observable though. So they do not change the observational fact of randomness predicted by QT and thus BM is just QT with the additional task to calculate non-observable trajectories.BM claims that fundamental objects (particles or fields) have some properties (positions or field configurations in space) always defined. That's what it means, according to BM, that things exist even without measurements.
That's what BM claims and all observations so far have confirmed the measurable predictions of BM with high accuracy.