Yes, I do think its possible to hit most of the major sites of Zaragoza in one day, although you may be exhausted by the end, but you will have the train ride to Madrid to recover. You could follow something along these lines (with estimated walking times):
Arrive early in Delicias station
Walk to Aljafería Moorish Palace (15 min walk)
Take Bus or Walk to Basilica del Pilar (20 min)
Walk along the Ebro Riverside area (next to Basilica)
Visit next door Caesar-Augusta Roman Forum (2-3 min walk)
Next walk to the Goya Art Museum (10 min away)
Have late lunch in El Tubo tapas-quarter (10 min)
Walk to Caesar-Augusta Roman Arena (5 min walk)
Taxi back to Delicias station
PS: There is all-day luggage storage in Zaragoza-Delicias station: https://community.ricksteves.com/travel-forum/spain/zaragoza-train-station