What an important question! Ever since Abraham and Sarah had to use a surrogate (the Egyptian woman, Hagar) to give birth, we Jews have had issues with building families and fertility. Even during the time of the Talmud, there were people who understood marriage and fertility as two separate issues.
A bayit ne’eman b’Yisrael – a faithful home among the Jewish people – presupposes a married life with a Jewish mother and Jewish father rearing authentically Jewish children. Not every home in all circumstances is blessed with two parents. A father tragically might die at war or of a disease before his child is born. There could be a divorce, G-d forbid, with the father gone thereafter most of the time, whether by court order or by abandonment. Other scenarios similarly could account for de facto one-parent households. Nevertheless, despite an eroding secular American culture dating back to the “Murphy Brown” episode where a fictional television character was characterized approvingly and then adulated in magazines as portraying a new social era where unmarried women could bring babies into the world without fathers as parenting co-partners, Judaism deeply discourages the notion of an unmarried woman having a baby through artificial insemination. Any outlier case would need to be presented privately to a properly trained and learned rabbi, who could determine whether enough uniquely exceptional factors combine to justify otherwise. It is hard to imagine how such an exception could be validated, even in a most outlier set of circumstances. The preferred approach might be to adopt a child and bestow upon him or her a warm home environment, rearing that child with the loving maternal instincts you would proffer.
Your heartfelt question raises two different issues: one about the acceptability of IVF and a second concerning single parenthood.