  We investigate rarely explored details of supercooled cosmological
first-order phase transitions at the electroweak scale, which may lead to
strong gravitational wave signals or explain the cosmic baryon asymmetry. The
nucleation temperature is often used in phase transition analyses, and is
defined through the nucleation condition: on average one bubble has nucleated
per Hubble volume. We argue that the nucleation temperature is neither a
fundamental nor essential quantity in phase transition analysis. We illustrate
scenarios where a transition can complete without satisfying the nucleation
condition, and conversely where the nucleation condition is satisfied but the
transition does not complete. We also find that simple nucleation heuristics,
which are defined to approximate the nucleation temperature, break down for
strong supercooling. Thus, studies that rely on the nucleation temperature
$\unicode{x2014}$ approximated or otherwise $\unicode{x2014}$ may misclassify
the completion of a transition. Further, we find that the nucleation
temperature decouples from the progress of the transition for strong
supercooling. We advocate use of the percolation temperature as a reference
temperature for gravitational wave production, because the percolation
temperature is directly connected to transition progress and the collision of
bubbles. Finally, we provide model-independent bounds on the bubble wall
velocity that allow one to predict whether a transition completes based only on
knowledge of the bounce action curve. We apply our methods to find empirical
bounds on the bubble wall velocity for which the physical volume of the false
vacuum decreases during the transition. We verify the accuracy of our
predictions using benchmarks from a high temperature expansion of the Standard
Model and from the real scalar singlet model.
