It it clear how Contraceptive availability (and willingness to use it) could see an increase in out of wedlock sex, and thus pregnancies due to imperfect use and effectiveness, but it is not so clear that legalised abortion could have that effect.
Are you considering that the availability of legalised abortion increases the perceived freedom to engage in out of wedlock sex (given it offers a means to “deal with any accidents”), but when push comes to shove, the affected women do not pursue the abortion - leading to increased births?
My understanding is that there is considerable demand these days from persons willing to adopt newborn babies. Thus any stay in an orphanage or foster care for babies is usually brief.