Has he got a potty tray? Syrians will use one - they can have very good and clean toiletting habits. They will pee in the litter tray and then you just need to empty it once or twice a week (I put Chinchilla sand in it - soaks up the pee). They will use it if you put it in the right place! Or what they decide is the right place. They usually choose a corner of the cage as a toilet so if you put it in that corner they'll use it. If he hasn't got a visible toilet corner at the moment, he may be peeing underground. So I would then just put the litter tray somewhere near the house and he might start using it.
When they're babies and quite young they do sometimes pee in the nest and then yes it has to be cleaned out - but that usually stops them peeing in the nest as they are very precious about their nest and hoard. Once they're a few months old they usually have very neat toileting habits and one place to do it in. The poops aren't much of an issue really - they're like dry seeds and not dirty or smelly (and they can eat them sometimes which is normal) so you can just spot clean some of those out if there get to be quite a few around the place.
At the moment though - as to how long to leave it - rule of thumb is - wait till you can smell something! Then it's a case of feeling around under the substrate to find a damp area and taking the odd handful of damp substrate out and sticking some new in to replace it (which is basically what spot cleaning is).
Life gets much easier when they use a litter tray! The rest of the cage stays clean and dry - although he may pee in his wheel sometimes.