It won't damage them, but it's not the gentlest start. Reaching for a bright phone the moment you wake, often in a dim room with sleepy, dry eyes, can feel harsh and trigger a bit of strain or squinting. It's the brightness-and-contrast mismatch, not the blue light, doing that.
Ironically, morning is when blue light is good for you, bright light helps wake up your body clock, so you don't want to block it. Just ease in: open the curtains or get some real daylight first, keep the phone brightness reasonable, and give your eyes a moment to adjust before diving into the screen.