Salzburg to Krakow for Auschwitz tour

You sound like you're pressed for time, so the train is not an option due to the distance between the two cities. Check flights instead.

If substitutions are allowed, then I'd visit Mauthausen, instead. Train connections are just over 1.5 hours each way, with a transfer at either Linz or St. Valentin. See www.bahn.com.

Flights from Salzburg to Krakow require connections, so you might prefer a nonstop flight from either Munich or Vienna. Try www.skyscanner.com.

The shortest flight I found on Google flights is about 2:40 each way, with a short layover in Vienna. I couldn't find any nonstop flights. Airfares are between $350 and $400. Lower fares seem to require long layovers, which you don't have time for.

But you may not find a schedule that allows you time to tour Auschwitz. The tours I see are more than 6 hours. So if you go first thing in the morning, you'll need to find a late flight back to Salzburg on the second day. And you'll need to figure out what to do with your luggage.

The only reasonable flight connection from Salzburg to Krakow is via Vienna by Austrian Airlines. A return ticket will be about $700.
Check here: https://www.kayak.com/flights
Don't forget to consider that Auschwitz is about 40 miles away from Krakow.

If you want to go by train, it is faster to go from Salzburg to Auschwitz (7:30 hours) than to Krakow (8:40 hours). You will have to change trains three times.

If you could spare 2 nights, you could take a night train to Oswiecim through Vienna Hbf, leaving at 7:00 pm, arriving at 5:00 am (!), and returning at 11:50 pm and arriving back in Salzburg at 9:52 am.

Thank you for your help. I greatly appreciate it!