How to make my browser to use a specific Random value for TLS Client Hello

As part of a CTF question, I want to block TLS connections which does not have a specific pattern in their Client Hello Random Number. Well, It is easy to block these connections using a combination of linux IPTable + NFQueue + a simple Python program.

The question is that, how the competitors can force their browsers to use a specific Client Hello Random Number which match the pattern (Let assume that they found the pattern)?