What is the expiation for the sin of engaging in a relationship that resulted in pregnancy outside of marriage, and does this pregnancy become permissible after a legal marriage?

First, you must repent to Allah and regret the sin.

Second, if the pregnancy becomes apparent before the marriage contract, then it is obligatory not to contract the marriage until the woman gives birth, because this pregnancy is not attributed to you, and because a pregnancy resulting from adultery is not attributed to the adulterer according to the majority of jurists.

Some scholars, including Shaykh al-Islam Ibn Taymiyyah, have held that the adulterer can attribute the child to himself if the woman was not legally married to anyone else.

The majority of scholars based their view that the child of adultery is not attributed to the adulterer on what was narrated by Ahmad, Abu Dawud, and Ibn Majah from Amr ibn Shu'ayb, from his father, from his grandfather, that the Prophet, peace and blessings be upon him, ruled that the child of fornication is not attributed to the fornicator.

What appears to be the case, and Allah knows best, is that you can attribute the child to yourself in your situation.