I'm certainly no expert, not by a long shot.
But basically a spore is like an offspring, and each offspring can have slightly different traits. So when you inject a syringe into grain or vermiculite, you don't really know A, How many different genetic variations will colonize the cake, or B, how productive those variations will be. Some mycelium doesn't produce many mushrooms, and some will be heavy fruiting.
What friends of mine do is inject the spores from the syringe onto Agar first. After a week or so they will be able to identify strong mycelium on the Agar, and what they are looking for is the junction where to seperate spores have germinated, and their mycellium has grown into each other and connected. That exact location where they have connected will be cut out with a scalpel and transferred to another Agar plate to continue growing. From there, they will select and cut out strong pieces of rhizomorphic mycellium and transfer them to seperate Agar plates.
These plates once fully colonized will be cut into about 8-10 wedges and each wedge placed into a jar of sterilized grain to make grain spawn. Which is then bulked to media in a monotub or shoebox.
From there, the most productive fruits are cloned to agar and the strain is isolated.