That just pushes the problem back to whether perfect circles can exist in reality.

Except that the length of a real objects can never be defined exactly. You can only give probabilities, eg. it has an 80% chance of being X or more units long, a 5% chance of being X or more etc, etc. At an extremely (an I mean very very extremely) low probability an atom is the size of the sun.

When things interact they also do it by probabilities. The lower the probability, the longer it takes to interact. (i.e. bring two deuterium nuclei near each other - will they fuse? Well, it depends on how close they are, the closer they are the less time it takes, since there is a greater chance that they are in the same spot at the same time.)

So in some sense, that's what time is.