AVE - Madrid to Seville: advance purchase or walk up purchase?

Are you saying you haven't booked a flight? Once you know your arrival time, then book a time to Seville you know you can make. I have flown into Madrid several times and it took me longer to walk to passport control from my gate than it did to pass through. No more than 10-20 minutes. However, I don't check a bag. Figure at a minimum of 2.5 hours to get from Barajas to Atocha , deplane to train.

I'm not sure. Our Best of Spain tour a couple of years ago ended in Seville and our return flight left from Madrid. We planned to take the AVE from Seville to Madrid and purchase walk up train tickets. Our RS guide cautioned against it warning that the train was full sometimes. He helped us buy tickets online a few days in advance.

Strongly recommend advance purchase as you can also get better pricing with advance purchase. Add three hours from time your plane arrives. Don't sweat having extra time at the train station as it is a wonderful place to explore.

Once you know that the flight is going to arrive on time for sure then by the ticket. You can do this using the ap on your phone right after boarding your flight. Give yourself 3 hours to get some refreshments and use the toilet so you are not rushing.

There can absolutely be full express trains on the Madrid-Seville line. I see them often enough when I check schedules to respond to posts here. There is some risk of multiple trains in a row being sold out if you wait until you land in Madrid to buy your arrival-day ticket. I think it's just a financial question whether it's smart to pay extra for a ticket that can be changed if your flight is delayed, because you won't be able to change to a full train any more than you'd be able to buy a ticket for a full train.

Although Elige tickets have some advantages over Basico tickets, if you need to alter your departure time, I don't think the change fee (20% of the ticket price) is the only thing you'll pay. The normal policy in a ticket-change situation is that the passenger must also pay the additional cost of the new ticket, which could be substantial because you'd be looking at day-of-travel pricing--though the Renfe website doesn't seem to explicitly address that.

There's a train station at Atocha Airport. You can head there after clearing Immigration and get a ticket to Seville if you decide to wait. They won't sell you a ticket for a departure you cannot make.

What you must not do is plan to buy the Seville ticket at a staffed counter at Atocha Station. You would definitely miss a lot of trains while standing in that line.

You can take a look at the schedule for that local train (Aeropuerto-T4 to Atocha) here: https://www.renfe.com/es/en/suburban/suburban-madrid/timetables. There appear to be 4 trains per hour on weekdays. It may be different on weekends, so check your travel date.

then taking the Metro from Barajas to Atocha

Apologies for not answering the actual question in the post (and feel free to ignore if you already know this!), but I noticed this and wanted to suggest that instead of taking the Metro from the airport to Atocha that you take the Cercanías -- it's a straight shot on line C-1 or C-10 from Aeropuerto T4 station to Atocha (see map), with a journey time of about 30 minutes.

This is especially because during the time that you are traveling (March 2022), there will be construction on Metro line 8 (i.e. the line that runs to the airport) that will take out the stretch of the line between Mar de Cristal and Colombia, which would force you to either take a free replacement shuttle bus at Mar de Cristal or to transfer to line 4 (which also does not go to Atocha).

Many, many thanks to all of you for your suggestions and comments. While I’ve flown into and out of MAD Barajas many times, I’d never traveled onward via the AVE (generally, a rental car or connecting flight). I’ll advance book the AVE via the Renfe site. And, a BIG thanks for pointing out the Cercanías option over the Metro during the period of construction.
Safe travels, everyone.