We're not actually allowed into the school, but we have to take the Reception children through the main junior and infant playgrounds, through the Reception playground and wait just outside the classroom doors and they are always late taking them in. 
I think a lot will depend on your pup's character. Some pups are independent and happy to be left, others, like Pip, are quite needy when they first come home and need a lot of reassurance that you're not going to disappear and never come back, so take a little time to get used to being left.
Mind you, Pip has surprised me this morning. Dh went out and massacred the greengage tree last night, removing all the fruit, but it was too dark by then to check for windfalls and pits on the ground. So I was out there at 8.00 am with my rubber gloves on grubbing around in the grass to try and pick up every last bit. Pip came out with me for a while, but then came back in and curled up in his crate. I reckon it took me over half an hour, so he's obviously getting much better at being on his own for a longer.
I then had to sort the dcs out upstairs and he was awake, but sleepy in his crate and didn't make a peep then either.
I was woken up at 2.00 am this morning by the lovely sound, over the baby monitor, of Pip throwing up in his bed. Dh went downstairs to sort him out and didn't come back, turned out he'd fallen asleep on the sofa. He let Pip out for a wee, then lay down while he waited for him to go back to sleep and went out like a light.
Apparently it was just a bit of bile, but I'm fretful, because I'm pretty sure he necked a greengage yesterday when he thought I might take it off him. He seems fine this morning though and is eating, drinking and pooing normally.
Sally Schmackos are horrible things, full of fillers and colours, it could well be that. FIL gave one to Lurcherboy a couple of weeks back. Even he had a bit bad stomach afterwards and he's normal got a cast iron constitution.
If I were you, I'd give everything except real meat and his normal food a break for at least 24 hours, then reintroduce each thing he's had one by one, so you can work out what he's reacting to. It could be the philadelphia, some dogs don't do well with dairy.