We have already reached the point where matter can get no more fundamental. In order to find out what is inside a quark you need to smash it at high energy (or supply enough energy to pull it apart) to see its constituent parts. This has worked great to find the quarks in protons, the protons in nuclei, the nuclei in atoms etc....
However, with quarks we have reached an interesting impasse such that we can go no deeper.
A proton has 3 quarks, and mesons are quark-anti quark pairs (hence they are particles containing 2 quarks) that mediate the strong force)
When you try to supply enough energy to pull a single quark out of a proton (in order to then isolate what's inside it) you have to supply so much energy that (by E=mc2) you are supplying enough energy to create two new quarks (or anti quarks).
So when you pull hard on the one quark inside the proton, you give enough energy to create another quark to complete the proton, and an anti quark to combine with the quark you are pulling on turning it into a meson that comes away in your hand.
The harder you pull the more particles you create of a type that you already know. Since we can never isolate a single quark we can't find out what's inside it.
If, when you add more energy you just keep making particles you already know, you can't go any deeper....you're at the bottom.