Sometimes it’s not actually the cleat itself but part of the sole of the shoe moving slightly against the pedal as you rotate the cranks. This is often the case if the SPDs are set fairly loose.
Apply a little chain lube to a cloth and sparingly wipe the parts of the sole which are in contact with the pedal before setting off and see if this helps.
If you’re using clumpy MTB winter shoes also check that the side of the sole isn’t touching the cranks as they rotate.
Keep an eye on your feet as you pedal, if you notice that your feet are making significant, rhythmic left to right movements as you rotate the cranks this can be an indication that your bike fit is not quite right, check things like seat height, cleat position etc.