"ideal citizens" were ought to be created from the kids who have survived infancy. Baby milk was not invented yet so, most likely, you wouldn't survive without a tit.

There were attempts to find a solution. It is explained in great detail in the 1907 edition of the Brockhaus and Efron encyclopedia (Брокгауз-Ефрон) article on foundling hospitals (Воспитательные дома). Short summary for those who don't speak Russian:

Between 1764 and 1768 nearly all of the foundlings have died due to a lack of wet nurses; the funding didn't suffice and the house was advised to sustain itself by employing the other kids in profitable enterprises. To keep infant lethality down they decided to distribute children to peasant families which already had children in addition with a pension while the child was alive. In 1770 the house was copied for St.Petersburg; similar Foundling homes were founded in elsewhere across the Russian empire.

In 1853 there was a complaint from the State Secretary of the Great Duchy of Finland that peasant-suckled children would still perish, and that their presence was spreading syphilis. Inquiry resulted that syphilis was indeed spread from an infected child to the foster mother and to her other children; that unmarried women "resorted to lascivious behavior in order to become eligible as foster mothers"; that they would neglect their own children for the sake of keeping the adopted child healthy. That lead to a ban on peasant adoption in Finland which raised the foster home mortality back to the old ~75%.