Hello Ceci :),
If I understand correctly, app installation is blocked on your device, and you would like to connect your Sony WH-1000XM6 headphones to your device without using the Sound Connect app. Let me know if I have misunderstood your concern.
Most Bluetooth headphones can be paired directly through the device’s Bluetooth settings, so the manufacturer’s app is usually only needed for updates or extra features. The exact pairing button or sequence depends on the headphone model.
Here's what you can try:
Press and hold the Bluetooth button on the headphones for about five seconds until you hear “Pairing” and the blue light starts flashing.
On a Surface, go to Settings > Bluetooth & devices > Add device > Bluetooth, then select WH-1000XM6.
If this is not what you are looking for, please clarify which device you want to connect the headphones to and what happens when you try.