Given that knowledge they can try breaking those pieces of plastic apart to see that it's a housing over some sort of ceramic core. Using spectroscopy and chemistry you can figure out what that core is made out of. Now you know what mix of chemicals allows for really high density data storage and computation.
Using x-rays and microscopes they can figure out that the little ceramic die has some sort of structure etched on it. Maybe remove tiny pieces to see what different parts/layers are chemically composed of.
Now they know that there's something interesting about certain elements deposited on top of silicon using some sort of etching approach. Early transistor research was already well along (and had been patented already in the 20s) so it's likely they would have made the connection. Given all that you can start brute forcing industries and ideas around those materials.