I've raised spotted larvae that were a few weeks from maturing (with legs), not ones that newly hatched. My suggestion would be to start them once they have legs with small amounts of live blackworms, and perhaps some frozen bloodworms. As they are nearing adulthood, they will eat like crazy, so you'll need to feed more often and perhaps larger amounts. Chopped earthworms are good too if you can find any.
Mine had access to water longer than usual and were kept at cooler temps, and coincidently they matured later than usual, and were slightly bigger than larvae who were kept at higher temps with less water and less food.
In the wild when their vernal pools start to dry up that triggers them to become adults, in only a day this can happen because once the pools dry up they will die if they depend on gills. I've been by wild spotted breeding pools and and observed this happening. The young adults hid under moist areas close by the pools, then a heavy rain came and they all scattered into the wooded areas.
So my guess is that mine took longer to mature because their water level was stable and they had plenty of food, so the trigger to rush metamorph didn't occur and they took their time to mature, thus being larger in size and healthier.
When they first mature sometimes not all of them will eat, some do better than others and i've had more than half die in their first week. Though the ones that did survive were very healthy.
I started mine on fruit flies and live blackworms, blackworms which I placed in a shallow dish. At first the young adults were very active on land climbing over everything and up the side of the tank, and still going in the water once in a while, they didnt care much about eating. In about 2 days though they settled down, and started digging under the substrate and hiding under fake logs I had in the tank. They would sit and wait for prey to come by them, then ambush it. After a good week of eating I upgraded them from flies to pinhead crickets, still giving live blackworms. In a month they started eating small earthworms which is their favorite.
They tend to beg to eat, and will eat anything you put in, so be careful not to overfeed.
Except for feeding time they are usually lazy and hide most of the day.