Unfortunately satellite phones are such niche devices that there's not really any way to do it except by buying a commercial device. Even a "DIY" device would in reality be a series of commercial off the shelf modules - unless you had those to hand then you'd need to get them delivered, which means you might as well buy a commercial satellite phone.
If for some reason you could buy the bits, you could probably piece together a communicator with a satellite modem module (https://uk.rs-online.com/web/p/rf-modules/2131335) and a microcontroller or single board computer. It seems pointless to bother though - why not just buy a Garmin or Spot for the same price.
You could replace the modem part with a software defined radio (SDR) - that's generic enough there's a distant possibility you'd find one locally in an LTE base station or some other commercial radio device. However, the software effort to implement the satellite modem protocols would be immense - basically impossible.
Satellite phones are also so niche that they'd draw a lot of attention to the user - something you probably don't want if you're in a combat zone.
A better bet would be to make use of the equipment you probably do have - cell phones, wifi access points, ethernet cables - to extend the reach of places which do have internet. That would require there to be connectivity somewhere, which you could then expand out using point to point wifi networks. You could make a long range WiFi antenna using a parabolic satellite dish and a USB wifi adapter or wifi router. If you can find cellular connection on a rooftop you could bridge it to the ground via a couple of wifi access points and a long ethernet cable.
There's also apps - eg https://briarproject.org/ - which allow for message passing over local WiFi or Bluetooth networks. Realistically there's no magic bullet though.