I asked the PCB manufacturer to compute the impedances (50 and 120 Ohm for this first project) and they told us they do not perform any impedance calculations.
- If you need impedance controlled boards, do not use this PCB manufacturer. Every serious PCB manufacturer will provide you with the calculations. Of course, there are some factors - as they need to spend their time on the calculations, they would like to be sure, they will manufacture your PCB. Otherwise they may not be very keen to help.
Other option could be to check PCB manufacturer websites. Some PCB manufacturers may have "default" stackups with all the impedances calculated. For example try to have a look at Sierra circuits - they are expensive, but maybe their calculator could help you (I used their calculator long time ago, but I think their calculator should give you accurate numbers based on materials and their PCB manufacturing process):
https://www.protoexpress.com/hdi/hdi-tools.jsp