Please tell what is your platform? FPGA, uC, PC,... the solution will be vary for each contex.
in the FPGA, you can add a timer and read it at exit point of bootloader.
in the uC, first initialize timer then start bootloader. then at the exit point of bootloader read it. the start up time of uC is constant that mentioned in the datasheet, you should add this time to timer time to have time from power on.
another considration is exactly the powered on or when it was stable!