It's the wrong answer. Also, it's not just when you wake up - it's at various times during the night. The real answer is the sacral nerve: https://health.clevelandclinic.org/men-get-morning-erections-5-answers-questions

You'll notice them in the morning most because a) you're awake and b) you've had several hours for your bladder to fill, probably enough that you need to relieve it. This puts physical pressure on the sacral nerve, causing the erection. In turn, the erection closes the sphincter to the bladder more tightly because getting urine in the vagina during sex would change the pH and possibly kill sperm you have deposited/will deposit, which makes not tightening that sphincter an evolutionarily disadvantageous trait. This does make it something of a self-reinforcing cycle, though.