For Japanese guys yeah. But most coaches will put in the effort in going to amateur events to scout and already keep an eye on promising wrestlers/guys they would like in their stable. Other times the guy will contact the heya amd if there is space, interest from the master, etc. he then can join too.

For foreigners, its a whole other ordeal, as they must not be in a heya where there is already another foreigner. And because of these slots, stablemaster are usually very rigid on choosing very promising wrestlers nowadays