Yin yoga is good for this exact situation. I do it without getting out of bed usually (husband is a heavy sleeper). I read somewhere “vigilance is the enemy of sleep” and that makes sense. Yin yoga is designed to calm your nervous system and I find it does help knock me back out. Try to let go of unhelpful thoughts, if you think you need to remember something for the morning place a rubberband around your wrist to make you notice and remember in the morning then let it go.
If it’s so late (early?) that you might as well get up, a morning run, jog, or walk as the sun is rising is a very encouraging activity. It feels so happy to see the new day born, and vigorous exercise in particular (so if you can run instead of walk, do it) is invigorating.