AbsoluteTiming[
 nMax = NestWhile[# + 1 &, 1, Sum[k*9*10^(k - 1), {k, 1, #}] < 10^6 &];
 lst = Flatten@Table[IntegerDigits[k], {k, 10^nMax}];
 ans = Product[lst[[10^i]], {i, 0, 6}]]