NFC Antenna Design/Matching without VNA
If you copy the adafruit design, you probably only have to change/tune the parallel resonance caps C7 &amp; C8.
All the other components are just there for impedance transformation and you do not need to change that.
But C7 &amp; C8 define the resonance frequency together with your (custom?) antenna inductance (L). This is the sweet spot.
Even if you had a VNA, you would not necessarily be able to get better results than the try and error tuning approach. This is because the RFID card heavily detunes the resonant circuit when approaching.
You will notice that a little variation of the parallel caps do not influence the reading distance that much, once you found a good reading distance. The size and windings of your coil have a much bigger impact.