Even at the time Java had some great tools and IDEs (NetBeans, Eclipse) and both computers and the JVM were fast enough for any performance issues compared to fine tuned C++ to not matter much, especially for a game like Minecraft that didn't (at the time anyway) push the CPU much.
Java allowed Minecraft to run pretty much everywhere, including as an applet (very important in its early time) and it relied (and still relies) on LWJGL which provides access to the most common stuff you'd need to make a game (OpenGL, windowing, input events, etc) - and at the time it also worked for applets too (you needed to download the LWJGL applet code but it was signed by the devs so you didn't get too many scary messages).
I used the same tech (Java+LWJGL) at the time to make a few simple demos/games and it was quite easy to make stuff - e.g. i made this[0] in a few hours using Java, LWJGL and Eclipse on the iMac i had at the time.