If you are hand luggage only...this might be feasible, but there's no room for error and not room for an unexpected line at passport control.
You will have to walk the length of T4S, go through passport control, take the train to T4 Main (protip is to always use the elevator to/from transit train), get a taxi (which does sometimes get to have a line at that time of day), the trip to Atocha, then security for the train and finally boarding on the train platform.
I would say if you go very fast you're looking at 1h15 or so to get it all done so I would personally say don't do it. Especially since you don't know it that well so any small thing could mess up your plan. Just either fly or get the next AVE and watch the turtles for a bit in Atocha.