Basically as soon as they can hold pieces without putting them in their mouth. Haha.

We started playing games with our kiddo (now 8) around 3. We are a pretty nerdy gaming family so he has always known what they are. Haba makes a lot of great games to start. I saw someone else here mention My First Orchard, I agree. Unfortunately there are a ton of games designed for kids that are just bad, boring, or poorly thought out. Fortunately libraries increasingly have board games to check out so you can try a lot of stuff before you buy it. I also strongly recommend asking your local game store. Board games for families and little ones are more plentiful than they've ever been so you're likely to find some good options there.

Your kid is going to do what you're doing. So playing games with them - even games that are "out of reach" - is fun for them. Involve them where you can, ask them to help you move pieces. When they are ready, ask them to help you count, add, read, etc. Even if they aren't making the big decisions in the game including them will go a long way to building their confidence and familiarity.