UART, USB... on cellular cards
The "traditional way" to interface with a cellular modem (or Bluetooth modems, etc.) is via AT commands (modeled after the original Hayes AT command set developed for telephone modems back when) sent over a UART running at 115200 baud.

Since it sounds like you want to send data faster then that, you will have to either bump up the baud rate on the UART, or choose a different interface.  I have used one of the SL series Sierra modems in the past.  Looking at the datasheets for a couple of the Sierra modules, it appears you can only bump them up to either 230 Kbaud or 921 Kbaud.

Another option is to switch interfaces.  I know there is an AT command sequence to switch from the UART interface to the USB interface (and back). With USB you would have a much higher data rate available (either USB 2.0 Full Speed or High Speed).  I am unaware of any AT commands that allow you to switch the control interface over to either the I2C or SPI interfaces.  I believe they are reserved for use by the on-chip processor (some of the chipsets allow you to run your own code on them).