Hi Applejacki,
Thanks for coming to Apple Support Communities for help today with your new Apple Watch and band. It sounds like your S/M band isn't fitting the watch.
Have you seen this article? Change your Apple Watch band
"Make sure that you use a band that corresponds to your Apple Watch case size. You can use a band that's designed for Apple Watch (1st generation) and Apple Watch Series 1, 2, and 3 with Apple Watch Series 4 and later and Apple Watch SE as long as the sizes are compatible. Bands for 38mm and 40mm cases are compatible with each other, and bands for 42mm and 44mm cases are compatible with each other."
If the issue continues, the Watch would need to be inspected. In that case, please Contact Apple Support.
Have a fantastic day!