Is it possible to make a junction diode by pressing two pieces of n type and p type together?

No, a functioning junction diode cannot be made by placing two oppositely doped pieces of semiconductor in contact with each other. A functioning junction diode can only be created in one piece of semiconductor with oppositely doped regions in it.

However if you placed the two oppositely doped pieces of semiconductor in contact with each other and HEATED them until they just began to melt and joined becoming one piece, it is possible to create a functioning junction diode this way. But this is a tricky and not very reliable way to do it, especially if you melt it just a tiny bit too much you will completely mix the two pieces and lose the doping entirely.