Mom and Dad Parent moved into 2B Jasmine Suites with the dream of raising a large family. Dad was the stay-at-home parent, while Mom was the career woman. Their new home had the very helpful lot traits On Ley Line (big boost to the rate of twins / triplets) and Good Schools (boosted performance for kids in school). Right away, mom and dad visited the spa (placed at the beginning of the challenge in Newcrest), so mom could get a fertility massage (another boost to twins / triplets) and then returned to their apartment to "try for a baby," which was successful.
In the days while Mom was pregnant, she rushed getting aspiration points so she could buy the Connections trait, and later the Fertility trait. Mom's primary focus was trying to work a job that required as few hours at the rabbit-hole office as possible, so she joined the Social Media Career (at L4, the sim works 4 days a week for 5 hours). She spent the rest of her free time building the skills to get promoted even further, which paid off by the 3rd week when she reached L7 and worked a whopping 3 days a week for 4 hours. Dad leveled up his mechanical skills (to upgrade the bed - no wasting time sleeping!) and wellness skills (so they didn't have to waste time traveling to the spa for future fertility massages).
They had their first kids (twins) on Wednesday, and soon after adopted two more kids. There was a little trial and error at this point - admittedly, their first set of twins could have been raised to young adults by Monday (instead of Tuesday afternoon) if done more efficiently - but eventually, the parents employed the following strategy to meet the early age up requirements:
1. Coddle and coo at the baby to become good friends (for some reason, talking was occasionally received poorly, which resulted in a loss in the friendship bar)
2. Perform a combination of 3 feeding / cleaning interactions under "baby care" for the infant stage
3. For the toddler stage, all kids had the independent trait. Thinking was raised by watching, Talking was raised with Blarffy, Imagination was raised by one parent reading to the toddler, Movement was raised by playing and "taking clothes off" interaction, which made the kid energized, and Potty was raised with the toddlers repeatedly using the training potty chair.
4. For the kid stage, the kids maxed the mental aspiration. This helped with solve a couple other requirements as well. The kids already partly finished the "read with an adult for 2 hours" requirement from raising their imagination skill as toddlers (see point 3.) Raising their grade to a B was necessary as the other early age up requirement; and raising their grade to an A met the teen early age up requirement (as kids with an A grade automatically receive a B grade when aged up). To ensure that the kids spent at most 1 day to raise their grade to the next level, they always completed their homework, extra credit (if applicable) and at least 1 school project, with help from their parents if they had time. Furthermore, doing all of this schoolwork helped raise their mental skill to L10. Finally, playing chess with their twin / adopted sibling also raised the friendship bar, so the sets of siblings could become best friends with each other.
5. As soon as they were aged up to teens, the kids had already met the requirements (see point 4), so they were instantly aged up to young adults and moved out of the house
Stray observations
Luck may have been a factor - While Mom always had at least 2 fertility boosts (fertility massage, on Ley Line, or Fertility trait) Mom and Dad gave birth a total of 5 times, and had twins every time. This was very convenient for the age up strategy, above.
I intentionally started in winter, so that by the time the first set of kids were school aged, it was spring / summer, and the kids never had any holidays off from school
I also prioritized "trying for a baby" as soon as I moved out a set of kids, even if that meant delaying the adoption, as I suspected the 3 sim day long pregnancy cycle would be a bottleneck
Because the apartment was so small, I was constantly cycling furniture in and out of the family inventory. Those school projects really take up a lot of space!
The kids aspiration points were all used to buy sleep potions, which helped because there was never more than 2 beds in the apartment at any time