Sorry, I misinterpreted the situation a little bit. It sounds like you have both an STM32F4xx chip on the board as well as the STM32F103 chip you show in the schematic. In that case, your board won't run the same as a discovery board since the F103 doesn't have firmware (as stated earlier). The firmware isn't published. But:
You can still program the STM32F4xx chip on that board, but it will take a little more work. You can probably leave the STM32F103 chip on the board but it won't do anything. To program the STM32F4xx chip with an external debugger, connect the GND/SWDIO/SWCLK/NRST/VCC pins from the debugger to the board and it will show up in STM32CubeProgrammer and you can connect to and program it. You can use CN3 for these connections. The board will also need to be powered separately, such as by the USB.
(Soldering an STM32F103 chip with the firmware already on it is also an option, but at that point why not just use the discovery board you got the chip from.)