I get confused with the US knitting terminology and yarn weights, as I’m in Australia and more familiar with the UK terminology and weights. However, I have knitted with Bernat Softee and had thought it IS a sportweight yarn.
From memory its tension (or gauge?) is 22st to 10cm. The important thing is to knit your garment according to the recommended tension. Using a thinner needle that gives a tighter tension and therefore a smaller garment really isn’t the answer. This is because a yarn is designed to hang properly when knitted at a certain tension, and definitely looks better too. If you go down a size or so in needles you would certainly decrease the size of the garment, but the knitted fabric would not look or feel as nice as it should. It would probably lack drape and be rather firm in texture. Not something you want for a small baby.
If ever I want to make something smaller than the size a pattern gives me, I use a different, finer, yarn. I make sure that the gauge the yarn knits to is the one recommended on the ball band, but because the yarn is finer than in the pattern, the garment will be smaller. I then ensure the body and sleeve lengths are appropriate for the size baby I am knitting for.
So… I definitely don’t recommend knitting Bernat Softee with a gauge that has more stitches per 10cm than 22st.
Better idea… find another pattern. There are many lovely patterns for baby boys, that is if you don’t mind buying one. Look at the Sirdar leaflets. I think their range can’t be matched. Not their old fashioned styles, but all the modern current ones.