In the first 24 hours after birth, your breasts may still feel soft and can begin to feel more full and heavier due to increased milk volume after around 24-72 hours. After this time, breasts usually become quite full and firm, sometimes tender. When you get to around days 4-6, your breast(s) may still be quite full but probably softer between feeds.
Some discomfort is common when your baby first attaches to your breast, but this should generally settle quickly as the feed progresses and there shouldn't be any continuing pain.