When knitting pullover sweaters for babies and kids, it's important to make sure the neck opening will fit over the head.
Looking at sizing charts, 3 month heads are 15". Neck openings are 4.5". Yes, knitting stretches, but leaving one shoulder open is the answer for a sweater that won't be a struggle for mom and baby.
1 Plan Ahead
Before you start knitting the sweater, plan for the open shoulder
Knit the front and back pieces as instructed, removing the left shoulders (as worn) on waste yarn.
Join the right shoulder
Re-hang the left back shoulder stitches and knit in ribbing, flat rib or garter/seed stitch (by hand or machine)
re-hang the left front shoulder stitches and work the same style of band, adding buttonholes
Pick up the neck band, including the edge of the shoulder bands and work as directed in your pattern.
Let's say you knit 1/2" bands at the left shoulder. Overlap the front over the back and you will be adding 1/2" to the armhole opening. Depending on the size sweater you are knitting and the gauge of your yarn, you may be able to just work this into the sleeve cap seam.
If not, you may want to adjust the sleeve cap slightly or knit fewer rows on the garment pieces at the left shoulder.
2 Afterthought Method
You've knit the sweater pieces, added the band and realized that an open shoulder would be useful.
Knit the front and back pieces as instructed
Join the right shoulder
Knit and attach the neck band per the pattern
On the left back shoulder pick up stitches and knit in ribbing, flat rib or garter/seed stitch (by hand or machine)
On the left front shoulder work the same style of band, adding buttonholes
With a little thought and planning, adding a finished shoulder opening for a kids sweater isn't hard.