Counting starts with the simple things.
Inexpensive counting starts with a long sting and a set of beads…or even lots of buttons lying around. Help the child string the beads or buttons on the string and count as they string it. Then tie knots at each end and have the child count moving the beads from left to right and back again. Make strings of ten, so counting to higher numbers is easy.
Make different lengths and tie around their neck for a necklace. Make a small strand on elastic and tie around wrist for bracelets. Keep their minds active and busy so they won't be thinking about poking their eyes or rocking for entertainment. They can wear their entertainment.
Cupboards are also a great way to learn math, spatial concepts and stacking. Have your child sit on the counter after you go grocery shopping and have them place the cans of food in the cupboard. I can already tell you, they will want to do this over and over again. That is fine. It is worth the mess at first and the inconvenience for you, as this teaches so many concepts.
I used to have several drawers and the bottom cupboards of my kitchen just for small children who would enter our house. I had a large can of beans with a bowl and stacking cups. The child will get these out, open and start scooping from the can of beans and measuring into the bowl and vice versa. I did this with rice also. They have that lower cupboard full of canned goods and the child will pull them all out (you will have to help them at first to know what to do) then 1 by 1, place them back on the shelf, counting each can they place back in the cupboard. Depending on the size of your cupboard, the child should be able to stack 2 or 3 cans on top of each other. For beginners, the sides of the shelf are great to help support an off centered can, but they get good at this. Then they count the cans as they stack. They also eventually learn how many cans will fit in a certain space.
While the tiny child would be playing in the cupboards, I would be making dinner. Of course, if the child were 3 or more, the child would get up and help me. As you know their attention wane's quickly, so then they would go back down to the cupboards and continue to "play".
By building in things to do at the child's level and around what you already do, they quickly gain concepts about the world around them.