7 days in Andalucia by train

Except for that first night, that you have for Madrid, with the amount of time you have, I like the plan. Ideally, you'd have more time in Sevilla, but your vacation time is short. Some might say to do Cordoba as a daytrip from Sevilla, and that is an option, of course. But there is a lot to do in Cordoba and it is an atmospheric city. Its nice to be there in the morning and evenings when the day trippers are gone. One consideration is that the AVE, higher speed trains are somewhat expensive, yet, I don't like buying train tickets for my arrival day because air travel can be so unpredictable. If you do Cordoba first, that train ticket from Madrid would be cheaper. That said, we took the train to Sevilla from the airport (via Atocha) and caught a nice nap.

I would suggest that when you land in Madrid, keep traveling onto Seville, either by connecting flight or by train. You’re tired and jetlagged anyway, so the day is a wash and you might as well keep going (and you can nap on the train).
Something like this:

Monday – Arrive Madrid, travel on to Seville. Sleep Seville.

Tuesday – Spend the day in Seville. Sleep Seville.

Wednesday - Spend the day in Seville. Sleep Seville.

Thursday – Daytrip to Cordoba or sleep in Cordoba, depending on your preference.

Friday – Morning train to Granada. Spend afternoon in Granada. Sleep Granada.

Saturday – Spend day in Granada. Sleep Granada.

Sunday – Either one more day/night in Granada or train to Madrid (depending on if you want to spend time in Madrid or if it’s just to fly in/out). Sleep Granada or Madrid.

Monday - Spend the day in Madrid. Sleep Madrid.

Tuesday - Fly out of Madrid

You might find my trip report helpful: https://community.ricksteves.com/travel-forum/trip-reports/trip-report-spain-november-2023

I'd get out of Madrid on the arrival day and add the night you've saved to Seville. All three of those cities in Andalucia have multiple worthwhile sights, but Seville is the largest and really does call for more time.

Trains will whisk you from place to place on this itinerary much faster than a car. With the way the express rail lines are laid out, you can slot Cordoba anywhere you like in your itinerary (many trains between Seville and Granada go through Cordoba), but because of the timing challenge when buying a train ticket for arrival day, I'd tend to position it first, as Jules suggested. That will save a bit of money if you opt to buy the train ticket upon arrival in Spain. Alternatively, you can buy a changeable ticket ahead of time. In both cases you need to be aware that Spanish trains along that route do sometimes sell out, so if you don't nail down a ticket ahead of time, or if you find you cannot make the departure time of your pre-purchased ticket, there is some possibility you won't be able to get a ticket on the first train you hope to catch. This is unavoidable (given the uncertainty of flight arrival times and inbound processing speeds at Madrid Barajas airport), but I think it's a reasonable trade-off for being able to use a chunk of time on your arrival day to get to one of your other cities, saving some time on a later day when one hopes you will not be so jetlagged.

As for whether to head to Granada before Seville, or vice versa, I suggest looking at the train schedules to see if one direction seems to align better with the way you like to arrange your days on the road. There are a lot fewer fast trains running in and out of Granada. By comparison, the trip between Cordoba and Seville is very easy to schedule; you'll have lots of choices.

Ditto--unless you are flying in from Australia or something, pressing on at arrival is always my strategy. You could do Cordoba first since that is a shorter train ride, leaving Sevilla for last.

While Madrid is a nice city to visit, with seven days, I'd minimize your time there and concentrate on Andalucia. Like, I said, you could buy a less expensive ticket on your arrival day and go to Cordoba. For us, we just paid the full fare ticket and went immediately to Sevilla. We caught a nice nap, got to Sevilla around noon and had a half for day exploring. Of course it depends on your flight's arrival time.

It does make LOTS of sense to be in Madrid the night before your flight. We stayed on Puerta del Sol, and enjoyed a nice walk to the palace/cathedral/concert hall area. It was pretty with the night time lights and there was a lot of activity in del Sol