We don’t recommend a specific thickness of mattresses as the available research does not suggest that this is an important factor for SIDS. Instead, the key things that make a mattress more safe and reduces the chance of SIDS are that it is firm, flat and waterproof. As long as the mattress is not overly soft/fluffy or angled, it does not appear to matter how thick it is with regard to SIDS.
Hope this helps
Kate -Support Team