How can I make contact with the material if soldering is not possible?
There are all kinds of things that you can try.  Usually there's a trade-off between ease of use, and reliability.  

How about conductive epoxy?  Perhaps too expensive.  

Press-fit pin-in-board technology (pressing pins into PCB, and they 'swage' into place).  

from:
https://en.wikipedia.org/wiki/Swaging#Electronics


  "In printed circuit board assembly individual connector pins are
  sometimes pressed/swaged into place using an arbor press. Some pins
  have a hollow end that is pressed over by the arbor's tool to form a
  mushroom-shaped retaining head. Typical pin diameter range from 0.017
  to 0.093 inches or larger. The swaging is an alternative or supplement
  to soldering."


However, the pin and pcb need to be purposefully engineered for this.

Sometimes a solution for this type of problem is to locate another access point on the pcb that you can take advantage of, and solder a wire onto that location.

Ultimately the solution is to practice soldering, especially managing heat. Learn how to use heat-sinks to control heat flow while soldering.  Use the proper iron temperature and flux for the solder and materials in use.

Good luck,

Chris