I will be visiting Madrid next week. Looking at the Prado tickets website, no advance tickets are available in the mornings. Does this mean they are sold out? Is it still possible to buy tickets at the door if there are none available on the website? Because of prior commitments, afternoon times are not possible for us. What other options are there?
Does this mean they are sold out?
Yes.
Is it still possible to buy tickets at the door if there are none available on the website?
Yes. What you want to do is show up before the museum opens at 10am. Go to the ticket office on the northern exterior end of the Prado, facing calle de Felipe IV. You might have to wait in the ticket line for a bit depending on when you arrive, but it shouldn't be too crazy. Then, use the Geronimos entrance around the corner from the ticket office.
It should be fine, you may have stand in a line or two to get in, but it won't be crazy like the Louvre, or Vatican Museums, in my experience.
I did this tour in May: https://www.takewalks.com/madrid-tours/early-access-prado-museum-tour/
I see they have availability on Monday, Wednesday, and Friday next week.
It was an excellent tour. So great being in the museum with no one else around. The guide was very knowledgeable. After the tour, you can stay as long as you like and go back and see anything else you want. Highly recommended.
While maybe not an optimal solution, if all else fails go during the free hours.