Is it true that the steroid hormones in milk can cause young girls to reach puberty earlier?

No. There is currently no evidence that the naturally occurring hormones in milk are associated with early puberty.

Milk naturally contains tiny amounts of hormones, including steroid hormones such as oestrogen and progesterone, because these occur naturally in all mammalian milk. These hormones are produced by the cow and are not added during processing. The Australian dairy industry has banned the use of oestrogen drugs in dairy cows since 2008. When drinking milk or eating dairy foods, most of these hormones are broken down during digestion and not absorbed in their active form.

Speculation in the early 1990s that hormones in milk might be the cause of early puberty in children has led to misconceptions about milk. Current evidence does not support a causal relationship between naturally occurring hormones in cow's milk and girls starting puberty earlier.¹ In fact, there is no conclusive evidence that drinking milk or eating other dairy foods (or any particular food) is associated with early puberty.

Scientists believe that factors such as genetics, overall nutrition, body weight and other environmental influences play a much larger role in determining when puberty begins.

Before and during puberty, dairy foods can play an important role in supporting growth and development. The Australian Dietary Guidelines recommend that children aged 9-11 have 2.5 serves of dairy foods like milk, cheese and yoghurt each day and teenagers aged 12-18 consume 3.5 serves each day. These years are a time of rapid growth, especially for bones and dairy provides a rich source of calcium which support bone development and strength along with other important nutrients.

Reference 

1. Carwile JL, Willett WC, Wang M, Rich-Edwards J, Frazier AL, Michels KB. Milk consumption after age 9 years does not predict age at menarche. J Nutr. 2015;145(8):1900-1908.