I have started using Arduino Pro Micros recently, and sourced inexpensive clones from China.
Experience is that all manner of inexpensive small microcontroller modules from China are likely to have issues with the bootloader: it isn’t there, it is back level, not suited to the actual clock speed.
I have come to routinely install a current / known / working bootloader to avoid wasting time down the track.
The Pro Micro does not have an ISP header, and the QFN package does not suit a chip adapter, so the next option is an adapter that can connect to the board with no pins, male or female headers, top or bottom.
Above is an adapter built on a small piece of Veroboard. If you are ging to copy it, make it one row of holes higher. I did initially, and in a miscount of rows, I incorrectly removed the top row. The black mark identifies the pin 1 of the Pro Micro, and the adapter connects to the side with the /RST pin.
The headers on the adapter engage JP6, preserving the pin ordering, pin 1 to the black mark on the veroboard.
I use this usually with a USBasp that has a 3.3/5V selection jumper, and powers the target (ie no USB cable on the Pro Micro).
Now not all cheap Chinese knock offs use the ‘standard’ pinout, so check for compatibility before using it.
Remember that the Pro Micro bootloader has USB support in it, and you MUST use the version to suit the Pro Micro clock speed (8MHz on 3.3V boards).