Can I connect an xbox one controller to my android smartphone using a micro usb to usb c cable

Have you tried connecting the controller via a Micro-USB cable to see if that works ? Micro USB cables are often provided as charging cables for smartphones like Windowsphone and Android devices.

Yes bit you are going to not charge as quickly

The cable from the Xbox One Play & Charge kit is a standard MICRO USB cable (not USB-C).

The cable itself can't be too powerful. It's the host device that "puts the power into the cable".

But I can assure you: I have charged my phone, my controller and my power bank with that cable without any issues.

Just beware that your phone has to have a Micro USB connection. If your phone has a USB-C connection, you will need a different cable.

The Xbox One controller uses a standard micro-USB cable when you wire it to the console. This is the same kind of cable that, for example, many Android phones use.

Consider getting a USB extension cable with the cord you already have. Single USB cords can be 3-5 meters in length before the electrical signal degrades, but it can be repeated with an extension cable.

Also consider this: if there are power outlets closer to where you sit, you can actually plug your Xbox controller into a smartphone charger and let it charge from there. Typical 5V/1A smartphone chargers will charge the controller fine.

If the Sync button is not working, simply get a standard Micro USB cable, and connect your controller with the console.

Every controller you connect to a console via Micro USB gets automatically bound to that console.

Just be aware, that you need to use a Micro USB data cable. Some Smartphone charging cables with Micro USB connector only have power but no data lines connected (to save money). So a phone charging cable might not work.

With your controller connected, launch the Xbox Accessories App, and check if the controller firmware is up to date.

After you made sure the controller is up to date, and works with the USB cable, you can then disconnect the cable, and the controller should work wirelessly.