What are you talking about? Do you mean first few frequency bins, and setting the others to zero? That would be a simple linear-phase lowpass filter. And if you do the shifting properly then you will see that it has a positive group delay.

There are filters with negative group delay, however. But FFT is irrelevant for that and it's not a time machine either.

Non-causal filters can be quite useful, and can be realized when the entire input sequence is available. And if one puts in a delay line, then can work without needing access to future timesteps.

A bit harder to realize with electronics or mechanics than software though...