It s unlikely that any sapient species will have litter of 7-14. It requires a significant parental investment to raise and teach children. One parent, or even two for monogamous creatures, are going to have a hard time educating 14 children at one time.
This is an issue with R and K strategies vs sapience, which I have gotten into many times before. R strategies are about having lots of young, K strategies are about investing lots of energy into a few young. Intellect, and sapience, are entirely K strategies and are never seen in R strategy creatures in the wild.
The problem is that sapience is expensive. Feeding our brains are a massive percentage of our total caloric requirements, so just being smart is expensive. However, more importantly, intelligence runs counter to instincts. Creatures that are going to survive by dependent on intellect can not have as many instincts to drive them and must instead depend on learning how to do things (instincts still exist of course, but their more of a helper towards an end rather then a full instruction).
This means that sapient creatures, or any highly intelligent creatures, must start out more vulnerable when young. They will not have instincts to help them survive and hunt, and so until taught how to do everything they are worthless. In addition their only as capable as their taught, meaning that even if they are provided food and protection to grow older they are still going to be helpless as adults unless they spend enough time with their parents to learn how to do everything.
Thus parents of highly intelligent beings will have to invest a significantly higher expenditure into their children. Not only will they need to provide food, nourishment, and protection for longer, as the child grows to be capable of fending for itself, but they will have to provide time to teach and educate.
As a result intelligent creatures almost always have few, or only one, young at a time. This is not limited to sapient creatures, of which we have only one sample and thus can't really draw conclusions from, but for all intelligent creatures. Look at the list of smart creatures, such as dolphins and primates, and your see the same pattern, Intellect is inversely correlated with birth sizes across the animal kingdom. As intellect, and thus dependence on learning, grow this will be even more extensive.
I should stress the limitation is not just providing for food for so many young at a time, but providing time it takes to teach them, as each will require some degree of individual attention to be taught. Imagine a mother with 7 children. Even if she had food and diapers delivered to her house every day she is still going to have a very hard time with the kids because they require so much attention to be taught and raised.
However, food is also a limiting factor. Intelligent creatures tend to evolve in areas where food is less plentiful, or is only plentiful if one employes intellect to reasoning how to access trapped/hidden food sources. These are environments that do not easily support raising multiple children (either you don't have enough food for them, or your too busy figuring out how to access the food to watch the children). Environments where food is plentiful instead tend towards R strategy creatures that have a massive number of young and leave them to fend for themselves.
If you created a creature like the above they would likely evolve to have fewer young at a time, possible with shorter lengths of time between birthing new children, to allow greater parental investment into the young. As young with more investment would likely learn more and have a massively increased success rate in later life.
If you wanted creatures as you mentioned the most plausible justification for their evolution is that young tend to die early, likely due to predation. Many young would be birthed with expectation many would die. For a sapient species this would only work if smart young were better at surviving then stupid ones, even at a young age. Thus you could basically test your young out to see who is stupid enough to die, and thus not worth further investment, and who is smart enough to be worth continued teaching. This would suggest an enviroment where young had to defend themselves, possible due to smaller predators that sneak past single parents to attack young, and the young having to be smart enough to identify the threat and get away/warn mom etc to not be eaten. Alternatively if the mere act of traveling form A to B was dangerous in a manner where smarter young would be able to avoid that danger this could work. Imagine tree based apes in a world where predators lurked in the trees. They young would follow mom around, and those that were caught by predators or fell to their death because they did not pick smart routes across the treetops would die, and the rest were likely the smartest and thus the ones worth teaching.
In this case their growth would likely be unusual. I imagine quick growth sport early on, to reach the point where they can protect themselves against whatever threat usually kills the young (which may simply mean growing until their able to travel on their own to follow mom). After this original growth sport they will likely slow down their future growth and take much longer to reach adulthood.
Why would they take longer, because again it takes time to learn. The young are dependent on their parents until they have learned all the tricks the parents use to survive (and these must be taught tricks, if the creatures are not relying on their brains to survive they would not be sapient, or would evolve away from sapience quickly). Thus childhood will take many years (or even decades) to be complete for any truly sapient species. If it take less then a decade to learn enough to survive your species is not dependent enough on it's intelligence to justify sapience evolving.
Until the children learn the technique the parents use to survive they are an expensive liability to the parents. Thus the less food it takes to feed them the better, as far as the parents are concerned. This means it is beneficial for the children to stay at less then adult size when first learning, they cost less to keep (and with 7 children being raised for a decade the caloric investment is non trivial!). Once the kids have learned enough to begin fending for themselves only then would they have reason to start growing more rapidly. Notice humans only go through their later growth sports at puberty, which is the time we reach sexual maturity and thus likely the time that parents would have seen their children as adults and stopped investing as much effort in them in the wild (not so now, but for the vast majority of our evolution we were likely shoved out of the next around puberty). The children stayed small-ish until they had learned enough, then hit growth sports and sexual maturity in preparation to being kicked out and fending for their own food (since one person can feed themselves better then a parent can feed a dozen).
In any case I would not put adulthood any sooner then 10 years old.