My older son (now a senior in high school) was bored to death in Kindergarten - to the point he was tying his classmates' shoelaces together during circle time, and it was the teacher who asked if she could have him screened. He scored as gifted, but we ended up pulling him out of public school and placing him in private school throughout elementary school.
When we moved him back to public school for mid-school, we chose not to tell the teachers either. He was not challenged and went from a happy, productive student to a mis-behaving, defiant adolescent. The teachers and school counselor decided he was a ne'er do well, and I had to take on the administration and pull out all the stops at that point to get him placed in gifted classes. Once there, his behavior and grades improved dramatically.
So from my own experience, my thought is that you're right not to go in there right away and risking coming off as the pushing mom who is convinced their child is the bestest ever.
But I'd keep close watch on the pulse of what is going on in the classroom. If you see signs of boredom, it would be a good time if it were me to begin having some conversations about your own insights into your son's abilities.
Good luck with the new year!