Cosmological collapse, where gravitational pull overcomes the universe’s expansion, can create primordial black holes or other bound structures. The ultimate fate of such a collapse depends on the initial distribution of matter and its equation of state, as pressure counteracts the gravitational infall. Then, in the dust case, where there is no pressure, shouldn’t a black hole always form? In this talk, I will attempt to answer this question using numerical relativity simulations, discussing the challenges of this problem and the progress we have made so far. Additionally, as this is in full GR, it presents an opportunity to characterise the cosmological spacetime; therefore, I will also describe this using gravito-electromagnetism and Weyl invariants.