No. Although it's true that the risk of breast cancer increases as we grow older, breast cancer can occur at any age.
From birth to age 39, one woman in 231 will get breast cancer (<0.5% risk).
From age 40-59, the chance is 1 in 25 (4% risk).
From age 60Ė79, the chance is 1 in 15 (nearly 7%).
Assuming you live to age 90, the chance of getting breast cancer over the course of an entire lifetime is 1 in 8; the overall lifetime risk is 12.5%.