Question: Does Self Realization happen quickly or gradually?
It depends on the mind's receding; whether that is quick or gradual. The mind takes time to give up its attachments. In Realization, the mind is in the Self, and remains there in all circumstances.
Question: Can that happen without meditation?
Whatever draws the mind's attention will keep it out in the world. To go to the Self, it has to recede.
Question: If it's quick does that mean the soul is advanced?
In such a case it occurs because the soul is ripe. So in Shri Rama's case, the legend says that sage Vasistha spoke to Him for 7 days and at the end of the 7 days, Rama attained Nirvikalpa Samadhi. This was because Rama's soul was so ripe.
It is like wood which is dry catches alight so easily. If the wood is wet then it needs to be prepared, and then it can make a fire.