If there is a new baby on your "to shop for" list and you haven't a clue what a good and appreciated gift would be, you are not alone. All you realize is that the baby is too young for the fabulous toys that are available and they grow out of clothing so fast.
One thing to do without worrying too much about what to buy is to ask the parents for a gift suggestion. There's a chance that they really need something and you could supply it wrapped in bright Christmas paper. If diapers or formula is what they really need, it may not sound like an exciting gift, but you know that you will be helping them with something the baby really needs.
Another gift idea is something my teenage brothers gave my daughter when she was a baby. Her birthday is in August so she was four months old for that first Christmas. I was delighted to open that big box and find row after row of baby food jars. It makes a lovely gift. Don't forget to put some boxes of baby cereal in there if your gift choice is food, plus a huge variety of baby food goodies. The age of the baby will determine whether you put any junior food or meat in the box.
Another idea for an infant Christmas gift is to buy a savings bond for the baby. When it matures in the number of years it takes, the child will have a jump on a savings account if they do not already have one. There are various issues of bonds, so asking someone at the bank which one would best serve your needs is always a good idea.
Although very young infants will not "play with toys" in the traditional sense, there are a few things that would still make a good gift idea. One such thing is something that Gund sells. It is called "Baby Gund" and is part stuffed animal while the other part can be used as a security blanket. The "body" of the stuffed animal is made in a blanket-like material and as soon as the baby is able to hold things, this may become a favorite toy.
Also concerning blankets, consider giving a quality baby blanket as a gift. Many of them now are as soft as velvet and they make an excellent baby gift. Something else that is made with the same soft material now is a "sleep sack" for baby.
If you happen to find a CD of lullabies for babies, it would be a special gift. If the parent will be playing the music at bedtime or naptime, you won't want anything too "busy" to stimulate the baby. Many collections of music made especially for babies are simply orchestral and have no lyrics to distract.
Last but not least, it is a unique idea to give a special Christmas ornament for the baby, perhaps with "Baby's First Christmas" engraved. In fact, if this is a child you will be buying a gift for each year (i.e. close relative) you may want to start a tradition of giving a dated ornament along with your main gift each year.