You can be against junk science, but entertain the likely possibility he also did it.
The path is this: he is known to have shook at least one kid before, so maybe that's that happened again with the kid who died in his care. Doesn't mean there was an intent. Just that he shook too hard or the wrong way. So you ask a doctor you check for signs. Doctor says yup, totally SBS. The end.
At no point did he need to "escalate to murder", so there is no leap needed. It's all very straightforward.