We actually had no free public kindergarten when I was that age, so I started with first grade. Sounds like I didn't miss much.
No real education started until 1st grade, which is when they bothered to teach reading. 2nd grade started times tables, I think, third cursive, and so on. 1st through 7th could probably be taught in a year, if you were really motivated.
I could read by the time I got there, and we did cursive in second and by third we were on exponents, so I think you're probably right.
We had kindergarten, but it wasn't required and I didn't go.
I subsequently did well all through school. I don't think I missed anything at all. Somehow I figured out how to cut with scissors without their help.