SIDS is statistically likely in younger babies (90% of cases before 6 months). The risk of SIDS is incredibly low.*
There are some actions you can take to further decrease the risk. These actions make sense because they are very simple things to do (no soft mattress she can "drown" in, put her in her bed on her back, no objects she can cover herself with in her bed, such as blankets** or toys, etc).
These actions should be are taken because they are zero effort and they decrease an already almost zero risk even further. Because they are zero effort, it would be negligent to not do these.
Trying to somehow restrain or turn back a baby that starts turning in her sleep is far from zero effort, and has downsides as well, for near negligible upsides. Babys survive sleeping on their stomachs all the time. I've been told I did.
*The risk of a baby drowning before she's 4 is higher than the risk of SIDS. The risk of the child dying before reaching 20 years of age is about 20 times higher than the risk of the child dying specifically due to SIDS (source).
**Use a baby sleeping bag instead of a blanket.
P.S: You said she sleeps face down. I assume this means the face is to the side so she can breathe. If this isn't the case I suggest you contact your doctor. Putting the head in a position where she can breathe is a natural reflex that should work from day one.