12 weeks is very early in the sleep development process. Your baby's brain is still sorting out being out in the world, and its too early to expect the sleep/wake cycles of an older baby.
My mom has a book on sleep studies that has a really interesting chart. It shows babies' sleep and wake times as dark and light bars on a 24-hour timestrip, progressing from birth to 6 months (?). It illustrates how at birth, they're just on and off, up and down, in short amounts, but that their awake time and asleep time gradually coalesce into longer stretches, most noticeably over the first 16 weeks. It really takes at least 4-5 months for a non-newborn pattern to stabilize, if not a bit longer. At 12 weeks you're still far from that point.
My first slept at least 3 hours at a stretch at night from birth, though he was an evening cluster feeder until about 9 weeks old. One night at about 9.5 weeks, he cluster fed and cluster fed ... and then fell deeply asleep around 9pm ... didn't awake when I put him down in the bassinet, and then slept nearly 5 hours. By 11 weeks he'd sleep about 6 hours straight, usually from about 11pm-5am. And by 4 months, when I went back to work, he was regularly doing 9pm-5am. And by the time he was a year old, that bedtime had moved back, on its own, to about 8pm. Sometimes it would look like he was not sleepy, but when we put him in jammies and nursed and rocked and did stories, he'd fall asleep. And if we ignored bedtime because he seemed spry? Well, one or two nights was okay - we could be flexible about it. But if it got ignored too long, it was clearly an issue. He was miserable, acted sleepy all afternoon but wouldn't nap at his usual times, and was generally negatively affected by it.
His sister didn't sleep more than 3 hours at a stretch until she was 15 months old -- but at the same time, she made it clear fairly early on that she needed to start one of those stretches by about 7pm. Again, if you pushed to keep her up, she'd stay up, but if we did it too many days in a row we saw a difference in her sleep cycles and behavior.
So I do think at some level that "sleep begets sleep," in the sense that I believe that "overtired" is a real thing, that babies and small children can get so wound up if they are kept up too long that they then cannot sleep when their body really needs it. So I think it may be more "Lack of sleep begets lack of sleep."