The antenna used for the PICC project is composed of two rectangular patch antennas. They are fed from the side using an inset feed, the inset distance was found experimentally using electromagnetic simulations.
To replicate the antenna you can use the drawing and manually make the antenna using a laser cutter, CNC or even copper tape. Alternativly, you could use the supplied gerber file in the repo to order the PCB from your prefered PCB supplier, e.g. JLCPCB. The substrate used is 1.6mm FR4.
Once you have a the PCB you can solder on the two SMA connectors, use connectors like these.