Your assumption that the Bulgarian coaches have a feedstock of hundreds of thousands of lifters is very far from the truth - the whole Bulgarian population is considered to be around 7.3M people, which doesn't account very well for all emigrants living abroad. Out of these 7.3M only 16% (~1M) are aged 0-17 (I assume that 14-15 y/o is the usual age that a lifter starts training professionally). That means that at the moment there are around 100K teenagers (aged 14-15), out of which less than 50K are male.
During the past 20 years sports have lost a big chunk of their (state) funding and therefore the attractiveness for young uneducated kids have lowered substantially, further reducing the pool of athletes.
I consider the three most prestigious and popular sports for males in Bulgaria to be football (soccer), wrestling and weight-lifting.