I bought my 4 year old a 12 inch bike with training wheels, are the pedals supposed to move when the wheels moving, he pushes his front foot down but even with the speed the back one never comes up enough that he can push that one down.
12 inch wheel bikes like this one:
are designed so that the pedals will not turn just by turning the wheels.
They are designed so that when the rider pedals the wheels turn.
Once some momentum is gained the rider can stop pedaling and the bike will coast forward. The rider engages the brakes by pedaling backwards - this is a coaster brake.
There are many, many bikes in different colors and frame shapes with the same design.
Your bicycle was assembled incorrectly. Take it back to where you purchased it and ask that they fix or replace it, or take it to a bike shop to be assembled properly.
Let me also add a note in favor of @mattnz 's comment. Turning this into a balance bike may be the easiest solution. On the other hand, my child never took to a balance bike and needed outriggers.
I think my kids had similar difficulty in learning to pedal. My guess as to what you're describing is that even if the crank arms are totally vertical, he hasn't figured out how to push the top pedal forward to initiate the next pedal stroke. It might help to get him to point his toe down at the bottom of the stroke and point his toe up at the top of the stroke. This can help put force in the direction of rotation instead of pushing straight down towards the bottom bracket (where the cranks pass through the frame).
Hi I'm new here but in a similar spot
Our 12" bike has never had the pedals, crank or chain attached, I removed them on day two and created a better quality balance bike.
After that, you better check on the size of your 4YO as my girl at 4 1/2 is now too big for her 16", she took on that size just over 3 1/2. 12" balance bike was 2-3YO.
I am repurposing the 20" trek mtb for her but I need to replace the old twist shifter.
It's a fraction large but she does ride it ok, I think I'll change it back to the XC flat bar I used when my boy was riding it the same age.