According to the search results, the normal oxygen level for a baby while sleeping varies with age and activity. A study performed on 150 term, appropriate-weight-for-gestational-age, clinically healthy infants at an altitude of 1610 m (5280 ft) at 24 to 48 hours, 1 month, and 3 months of age found that mean oxygen saturation at 24 to 48 hours of age is 92% to 93% and varies little with infant activity. With increasing postnatal age, there is a tendency for increased oxygen saturation during the awake states to 93% to 94%, while oxygen saturation during sleep stays the same or even decreases slightly. The lower end of the reference range (2 SDs below the mean) is as low as 85% during feeding at 24 to 48 hours of age, and as low as 86% during quiet sleep at 1 and 3 months of age, with 88% to 89% the lower limit in other activities at all ages.
It is important to note that many factors can affect oxygen levels, and not all are concerning or even in your control. Higher altitudes contribute to lower baseline oxygen levels, and sickness, apnea, and nasal congestion can all affect a babys oxygen levels. Knowing your babys baseline oxygen level is a personalized approach to monitoring your babys specific oxygen levels, and following your babys personal trends will give you the best insight into your babys health and overall well-being.