I am aware of the advice from SIDS not to. However, I don’t care for SOME of the SIDS guidelines (I let my 8.5-month-old play with a plush animal and a lovey, for instance).
She cuddles up with the teddy a lot. Thus, I’m perplexed as to why they forbid pillows. She looks to be in love with one. Does anyone offer a tiny cushion to their infant?
Not my own. I’m too nervous to go against the SIDS guidelines, but that’s just me.
Likewise. It’s the scariest thing ever. I have to go check on her every time I hear her sleeping too soundly.
This is the URL for the pillow and sleep safety resource that was sent to us
I really appreciate this, I will look into this 
She would be tilting her head upwards, therefore it has to be a quite flat bear. As they get older, their ability to move around and breathe more easily makes them less susceptible to SIDS from items like pillows and blankets.
To address your question, though, my two-month-old daughter does not have a pillow; instead, she is loosely swaddled in a blanket.
She covers it with her entire upper body, in a sense 
I’m not sure how to respond to your query, but I believe you’re conflating suffocation, which is a fairly regular occurrence, with SIDS. But, it’s wise to be aware of the risks involved while using a cushion, for example.