Chosen Solution

Is it safe to power on an mid 2010 21.5” iMac without the display plugged in and after it started, plug in the display calbes? Thank you!

No. You risk blowing up the backlight circuit on the iMac’s logic board or display board itself. Edit: When plugging in or unplugging screen cables it’s best to do it if possible with no power source connected so that there is no power running through the logic board.