Asalam Alaikum. Mashallah I met a woman years ago she was 22, with a 5 year old child. Yes, she had a teen pregnancy and wasn't married. She had full custody. The Imam had called me as she wanted to know about Islam and introduced us.
Alhumdulillah over time she wanted to learn more and more. She would attend lectures at the mosque, some social events and I introduced her to many sisters. Alhumdulillah she embraced Islam.
Speaking with sisters, some expressed how difficult it would be for her to find a husband. To me, it was a blessing having a child already because it will weed out the insincere, the weak and the shallow. It takes someone sincere, strong and of good moral character to accept a child that isn't yours. A Libyan brother, never married before, approached her parents and her - she married. That was 17 years ago.
And the child out of wedlock?
At age 7, he was reading hadith and committing them to memory. At age 11 he had most of the Quran memorized. Now, in his 20's, he is halfway through professional studies, establishing himself for a future family inshallah. He has expressed wanting to marry a sister who already has a child, like he was - to give back the unconditional love and gratitude he feels for the man who raised him as his own. He learned this love from the man that married his mother.
And now the brother has a pious child that will pray for him. Some don't even have this, after marrying their virgin wives and satisfying the cultural charade, their kids don't behave as Muslims. May Allah guide them, Ameen!