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.
In both cases, the bootloader did not work. I did not investigate further but did note that the NVM user row looked like it had been cleared, but just wrote a new bootloader and restored a default user row with protection for the 8192 length bootloader.