Sleep help for exhausted 3 year old

[DinoDig]

Looking for some tips/advice with my 3 year old boys sleep. He started at preschool and nursery and since then we're having sleep issues in that we now have night wakes and early morning waking which I believe are classic overtired signs. They do try to get him to nap at school which he has done a handful of times. Most of the time he doesn't want to nap but when he does we generally get a better night.
On average he goes to bed around 7pm, awake from around 5am with a wake in the night too. Which wouldn't be so bad if we weren't all so tired! I know people will say just put him to bed later but my poor boy has grey bags under his eyes and often mopes about on the sofa when he comes home from preschool as he's so tired 😥
Any tips from anyone who has been through similar gratefully received

I'd actually say the opposite and try putting him to bed earlier, if you can, especially at the moment when he's probably getting used to the new regime.

Thanks @SiouxsieSiouxStiletto Probably a good idea. Maybe I'll try bedtime 6:30-6:45 and go from there

I'd agree with an earlier bedtime. For the early wakes, would he go back to sleep, or at least doze for a bit, if you let him come in your bed at 5am (or got in his, if it's big enough)? I appreciate some people don't want this, or allowing it once means it becomes something demanded all the time, but if it works, it can get them relaxed and cosy and so helps their bodies relearn that it's still sleep time.

How is it going?
We are in the exact same boat, and ours also started just over a year ago when my son started preschool (he's turned 3 September).
Started with early waking around 5am every day. Now we're as early as 4am plus multiple wakings most nights.
Becoming desperate and very exhausted.

@lolomoon how's he getting on at Nursery? Is he happy and settled or have they mentioned anything?

For the sleeping I'd try The Mo Cry Sleep Solution for Toddlers & Preschoolers.

Some simple things you can do though are to make sure he's warm enough. My DD slept better at this time of the year with a fleece blanket between her mattress and sheet. Making sure he has plenty to eat too. So if you don't already, offer him something like Ready Brek abs banana before bed.

I really sympathise though, both of mine are ND and sleep was very elusive for a long time