Resources on your homeworld are
always small in quantity-- usually around 30~50k of the most used minerals and a little less for some others.
It's quite common to completely mine out some minerals in the first few years.
However, there is an always some of EVERY mineral.
- don't build more manned mines
- convert those you already have to automated mines. Frees up more personell to work in other sectors (like research labs.)
- ship automated mines offworld with a mass driver and set up some automated colonies.
--and remember, just because your homeworld runs out of sorium doesn't mean you're out of fuel. Even the starting amount of fuel refineries will pump out enough fuel for quite a lot of exploration, but then again you need sorium for some parts of ship construction too iirc.
Once you get the hang of it you'll realize that you'll have a serious mineral crunch on some minerals (notably corundium and duranium, anything used for building up industry.)