One-way stretchy wraps are commonly available and can be a challenge to use well, due to the lack of stretchiness. Most one-way stretchy wraps will only stretch a little across their width, and not across their length (eg the Scottish Baby Box wrap), and lack "bounce" and the elasticity that is so useful in two-way stretchy wraps.
This photo tutorial with a one-way stretchy should help you gauge the space needed for your baby more effectively, and work with the fabric to achieve a safe, snug carry (the pocket wrap cross carry, PWCC). This is a “prepared PWCC” and is an option for smaller, more vulnerable babies who should be moved minimally from their secure chest to chest position, as well as for those who prefer to have things feeling snug early on.
Follow the steps to ensure a safe and snug carry; the time spent preparing really pays off when baby is put in, far less fiddling and adjustments and baby will be much less likely to sink as you move around or when they fall asleep.
Video of this process can be found here.
You can find videos of a more “adjust-to-fit” version of the PWCC in this YouTube playlist, along with some tighten-as-you go options (the front wrap cross carry, FWCC) that are more like woven wraps.
Read more about carrying newborns in two way stretchy wraps or Close Carriers here.