«lets assume there is an input that leads sha-256 »
Your assumption is wrong. Theoretically, there might be no inputs that are solutions to the PoW. Of course in practice there are almost always a large number of solutions, but again the theoretical possibility of it is why it is correct to say the PoW is memoryless.
Even if theoretically there was always a solution, there is no way to iterate sequentially over all inputs because after iterating over 2^32 nonces, miners have to change the 256-bit merkel root, which is effectively random. This aspect alone makes mining memoryless.
Your assumption is wrong. Theoretically, there might be no inputs that are solutions to the PoW. Of course in practice there are almost always a large number of solutions, but again the theoretical possibility of it is why it is correct to say the PoW is memoryless.
Even if theoretically there was always a solution, there is no way to iterate sequentially over all inputs because after iterating over 2^32 nonces, miners have to change the 256-bit merkel root, which is effectively random. This aspect alone makes mining memoryless.