Nope, it's all chance. There's a way to breed them though.

So the first thing to know is mycelium colonies ascience, which means they get old and die after a time. This means you can't just keep using the same mat and taking a culture and growing it over and over.

What you want to do is make a bunch of spore inoculations on agar in petri dishes, then take the best ones and clone them into several clones, like a dozen or two dozen, a lot. These clones are only the 1st reproduction you've done with the mat, so they're not even close to wearing out. But now you have a bunch that you can clone from. Keep them in a refrigerator, labelled.

Pick one of the clones, inoculate from it, save it. Do that until that clone is done, then move on to the next. You can basically keep a good mycelium going this way for a very long time, the limiting factor is how many initial clones you make, and that they do continue living under refrigeration, just at a much slower pace.

The approach some take is to make a bunch of spore inoculated petri dishes, then inoculate something with a culture from each one, see how it goes, then clone the shit out of the top performers into petri dishes and use cultures from those to inoculate until it runs out. Generally you can avoid a lot of wasted time by only doing this with ropy looking mycelium.