Since it's only 2 months old, it should have a warranty on it, so take it in and let someone else figure it out. This sounds like the very early stages of a MLB failure, possibly due to bad caps. It might also be a bad PSU, but either way, it's definitely a hardware issue.
I bought a new 27" iMac about two months ago and for the most part it is fine. It has 256G of SSD, so it is fairly swift at most things. I have a USB keyboard, but the original specced wireless mouse.
Every now and then, it will not start up.
Pressing the power on button at the back has no effect.
Unplugging it for 5 seconds and plugging in in again however allow it to start up as normal.
I always shut it down when I have finished using it.
I am puzzled as to why this is occurring.
Does anyone have any ideas?