The short version: If your kindergartner can count to 20 reliably and understands that the last number counted is the total, they're ready to start addition with objects. Begin with "putting together" using toys or snacks, not worksheets. If they still recount from 1 every time, give it a few more weeks of counting practice first.
All three don't have to be perfect. But if the first one isn't there yet, addition will feel like memorizing magic spells. Build the counting first.
Skip the plus sign for now. Put 3 crackers on the table, add 2 more, and ask "how many now?" Let them count all of them. That's addition. After a few days of this, introduce the language: "3 plus 2 makes 5." The symbols can wait until the idea is boring.
The best first problems use totals under 10, real objects, and situations your kid cares about: snacks, toys, points in a game. "You have 4 stars and you earn 2 more" beats "4 + 2 = ?" every time at this age.
Don't rush to memorization. A kindergartner who can chant "2 + 2 = 4" but can't show you with blocks doesn't understand addition yet; they've memorized a sound. Understanding first, speed later. The speed comes on its own in first grade.
Kindergarten math varies wildly, and that's developmentally normal. If your child is happily counting and combining objects, they're on track even if a classmate is already doing worksheets. If by the end of kindergarten they can't count a set of 10 objects accurately, that's worth a conversation with their teacher.
Make Ten Ladybugs builds the "pairs that make 10" foundation, and Cauldron Addition turns early adding into a game. Both start with objects and pictures before any bare equations.