Bath sink no overflow hole?

[Billbill84]

Hi guys. Our double vanity mast bathroom sinks don't have any overflow protection, there's no holes! I was wondering if maybe the installers forgot to predrill them? I've never seen this before on a bath sink.
I went under there to investigate drilling probability and found that the underside of the sink bowl has a plastic or fiberglass type of thing over the actual slate or whatever marble looking material the top of the sink is made from. I'm thinking the plastic feeling under bowl is a catch basin for water coming in from the overflow that doesn't exist. Also under there I noticed that flat area that the drain tube connects to is made from the hard slate like material that the top side is made from.
This plastic under bowl is weird so I'm confused if it's a overflow catch or what. So should I grab a small masonry bit and attempt to drill it out??

 

[Snoonyb]

The sink was obviously poured without the drain, so there is actually no economical way to create an overflow prevention, so, just live with it.

 

[Billbill84]

The sink was obviously poured without the drain, so there is actually no economical way to create an overflow prevention, so, just live with it.

That's what I initially thought BUT what's this plastic bowl over the bottom side of the "poured" bowl? None of the other Sinks have it and they all the same type of sink

 

[Snoonyb]

Beats me, In over 45yrs. in the trades I've never seen a sink, composite or cast, without an overflow prevention drain.