There is no general purpose compressor that can achieve compression on all random streams of bytes... but there is a possibility to compress a specific random stream of bytes, if you get lucky
You'd have to define what you mean by luck which would be equivalent to choosing some pattern that your compressor can recognize in a random stream of bytes and then computing the probability that pattern appeared in some random byte sequence. It's not a winnable game in any practical sense because whatever compressor you choose the probability of getting a sequence from your opponent that will conform to the patterns recognizable by your compressor is essentially 0.