Why the early universe had low entropy
In plain words
Entropy (a count of how many microscopic arrangements look the same) has been rising since the Big Bang, so it was extremely low at the start. Physics has no accepted explanation for that starting condition.
Precise statement
Explain, within a stated measure on initial conditions (Liouville measure, or a measure from a quantum theory of gravity), why the coarse-grained entropy of the observable universe at early times was far below its maximum (today approximately $10^{104}\,k_B$ against a black-hole bound of order $10^{123}\,k_B$), or show that the low-entropy initial state must be postulated (the Past Hypothesis). An answer is a mechanism that makes it typical, or an argument that none can.
What would settle it
A derivation from a specified theory of initial conditions that predicts the low early entropy and its form (nearly uniform matter, low tidal curvature) without assuming it.