He had broken out of prison. Remember, she mentioned 6 marshals kicking down their door to take him back. He has broken out of prison more than once

I believe she was college age so I could believe 18.
COOKIES AND MILK!-Ed

Does it say the daughter is only 18? I dont remember it ever saying her age

This is the best explanation. Mason says that He met her mother at a rock concert if that helps.

He went to Alcatraz in 62 but escaped in 63. He then escaped from another high security prison later with no date given. He originally went to prison in 62 and the film is set in 96 which covers 34 years meaning that if he spent a total of 30 years in prison he must have spent four years on the run which is more than enough to get someone pregnant

Zeppelin.

I love how he's casually going to a Rolling Stones concert while he's on the run from escaping prison.

He escaped from Alcatraz during that time, that's why they brought him in, he had inside knowledge about the place.
This can't be right. Since Alcatraz closed in '63. So his escape had to have been before then. In fact, not much of the movie since makes sense. Since Mason had microfilms with government secrets such as the JFK assassination and that was the reason they put him in prison for withholding those films. Yet JFK was assassinated after Alcatraz had closed, so none of the story makes any sense.

He escaped from Alcatraz during that time, that's why they brought him in, he had inside knowledge about the place.

Good question. Hmmm