Wait a while before buying a white noise machine. My guess is that they will not want it at the daycare, but aside from that she has only been there for 2.5 days!
My little one is 3 months old and her first couple of days at daycare were similar. Her teacher told my husband that every time another child cried she got upset. That lasted a week and then she got used to it.
Your little one needs to get used to sleeping through noise. Your house should not be intentionally silent while she is sleeping and in the words of my very wise pediatrician "Don't do anything to put them to sleep that you can't do anywhere and with anyone!" This is the BEST sleeping advice we heard and have lived by it! Like Jo W said, unless your home is unusually noisy, this is probably not a great idea!
If she's still not able to sleep in a week or so, talk with the provider about ideas or things they have done in the past. We sent in a swaddle wrap for our daughter because we were using one at home and it helped her sleep, so they will work with you if it's something "typical" and "simple".
Give it a little time!