"Spoiling" is a matter of definition, and so there's always a great deal of discussion on the topic. I think spoiling is giving in to a child in order to make it stop some deliberately manipulative behavior – teaching the child to misbehave to get what it wants.
But babies are not that deliberate, in my observation, for at least their first 5 or 6 months, and probably much longer for most of the ways kids can get spoiled. Babies' needs are always legitimate, to them, and they respond with distress when their needs are not met.
So the trick is to find ways to meet those needs without cutting into your own needs too severely, although we do well to recognize that for the first several months, NOT meeting a baby's needs will create more disturbance and disruption for everybody, and possibly mark the baby's personality in ways that will create additional problems later on. (It's hard to recognize that when you feel that meeting the baby's needs are already causing total disruption, but really, it could be worse.)
It has appeared to be true for both my daughter and now my grandson that spending a little time trying to understand any situation from the child's point of view brings helpful insight. Both of these babies napped best when sleeping on someone's chest for their first couple of months, which became a terrific burden for the caregiving adults (especially as they became heavier!).
I found that if I gradually introduced other stimuli, such as singing or a sound machine, gentle bouncing, tapping a back softly with my fingertips, etc., the baby would absorb those inputs as part of its comforting and relaxing signals. I was able to put both babies down very gradually earlier, withe the help of the alternate stimulus. With my daughter I also introduced a flat pillow between her and my body, to cut down on the heat and heart sounds she would get from me, and was able to lay the whole "package" down when she had fallen asleep. (Those were the days before SIDS became part of parents' vocabularies.)
There are lots of stories of babies getting "spoiled" and not making good transitions or fitting comfortably into their families. I can't say that that never happens, and I'm sure personality (of both parents and their babies) figures into the equation prominently. But the babies I have known who are most secure and adaptable have generally had their needs met consistently and ungrudgingly in those early months. That could be because they were the easiest babies anyway, not making heroic demands on their parents. But my heart sense tells me otherwise. Parents who are able to give their babies what they need tend to have happy babies. So the sacrifices you make for your child now will probably make parenting easier in the long run.
My best to you. It must be difficult to give your new baby everything you wish you could when you have other little ones tugging at you.