Cyclical universe
If we assume that the universe alternates between expanding and collapsing phases, with the entropy gradient reversing during the collapse phase, the need for a time-asymmetric boundary condition is avoided since the evolution of the universe is time-symmetric overall.
For this solution to work however a "future hypothesis" is required that posits that, after increasing during the universe's expansion, entropy would reverse and decrease during the collapse phase ensuring a smooth, low entropy Big Crunch. This was suggested by cosmologist Thomas Gold, with such a universe being known as a "Gold Universe".