The Sids and Kids official line is that if they are physically able to get themselves from front to back while awake, then not to worry. You still should put him down on his back, but don't fret too much about turning him over.
Last year due to someone over-interpreting the rules, we used to turn babies over at childcare, and none of them were sleeping more than half an hour. Until the sleep nazi coordinator had to help put children to sleep herself and realised how riciulous it was, and we got a consultant in.
The SafeTSleeps can be good, but I know a family with twins who used them and ended up being woken because of screams of frustration from one, and found the other (little acrobat) had managed to turn himself over anyway!
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