My 2 were both nightmares in the early weeks of starting preschool & School & I found that it was more important to have their "relaxing" activities than to worry about extra sleep as it was more the mental tiredness than physical tiredness that was in play, so things like longer or earlier baths, spending more time sitting & reading stories, snacks & big drink the moment I picked them up from preschool were more helpful than hurrying them along for early bed. Both have always been early risers & so they didn't tack sleep on in the morning, but would struggle with going to bed earlier because they could both read the clock from 3yo & so knew what time it was.
So for us it was more about managing the time that they were awake as opposed to trying for too big a change in times. That said both of them tended in those early stages to do a catch up nap on days they didn't go to preschool or weekend when they started school, often it would be in the car on an outing, but that was how the sleep got caught up.