Yea, the pressure increases as the black hole shrinks until tiny ones disappear in a massive explosion.

I do not know how the forces change over scale, though. For all I know, it 'could' be that early small black holes could've evaporated, but the early universe was also a lot hotter than now, making that point where they 'can' evaporate a lot smaller, too.

There is also the question of how homogenous the universe 'actually' is which throws a wrench into the maths as to whether it was possible. So even if the norm says no, there 'might' be a chance some less dense region saw a time where black holes could evaporate.