Numbers are a way to express mathematical relationships in our environments. Children first experience number through sorting and classifying objects, which is why having collections of objects in baskets or boxes is so important. Eventually children will want to count what they have and begin to notice relationships between quantities - which has more, which has less, the idea that an amount gets larger when I add more to it, that the last number I count is the number in that set, that I have to touch each object and only count it once to get an accurate count. All of these kinds of experiences happen without numerals or symbols being introduced. Eventually children can be shown the names of the numbers and play games associating quantities and symbols so that the idea that a numeral stands for or represents a specific quantity is understood.
A video that gives examples of counting games to incorporate into work or play with children. It highlights using mathematical language and materials to use as well.