The number of abortions fell to about 625,000 in 2016 according to a few sources using CDC stats. That was the lowest since about 1973 if we can trust the statistics. A women's health site pegs the current number closer to 1 million.
Abstinence is obviously the only birth control that is effective 100% of the time in today's America.
Prior to that, Abstinence, when practiced in Ancient Greece, was sometimes overcome by intervention from Zeus. Later in Imperial Rome abstinence was overcome by Jupiter and, in one notable example in Judea, by the Holy Spirit.
Assuming that humans have no self control, then effective birth control is needed.
Assuming that humans can guide their own actions, education could be helpful.
Can society overcome biology? Apparently, at least in some ways, it can. The Birth Rate in developed countries is way down.
If the number of abortions per thousand is down even marginally and the number of births per 1000 is way down, something has already changed.
Abortion statistics in the United States - Wikipedia