No. The short answer, is no. It's simply not a safe position for your baby to sleep in.
Carrying outwards facing has hugely grown in popularity over the last few years, but somehow this important piece of safety information has gotten lost.
So often parents simply don't realise that carriers can not safely support their baby outwards facing if their baby is asleep. Or they think - "well it can't be that bad. I've seen other babies asleep outwards facing...". And I do understand the attraction, babies around 4-6 months start really fighting sleep and will often really fight going into a carrier inwards facing, particularly when they are overtired and overstimulated and they'll shout and cry because they are tired. But placing them outward facing immediately silences their shouts. But it's hard for them to sleep in this position as it's really simulating and so that tired, overstimulated baby will become more tired and more overstimulated and that short term win quickly builds into a bigger problem for later.
Or they do actually fall asleep, and they lose tone, their head lolls and the carrier can't support them while outward facing. Because, unlike human hands, fabric doesn't know the difference between supporting their head and putting too much pressure on their windpipe.
So while outward facing can be a super fun position for a curious baby while they are wide wide awake, I really wish more parents knew it isn't a suitable position for a tired baby and that it can be an actively dangerous position for sleep. If your baby is tired, or falls asleep please turn them inward. Yes they may well yell at you for a bit, but get walking, get swaying, get moving and I promise they'll settle down and you and them will have the comfort of knowing they are in a supported, safe position for their nap.
And if you are struggling to get them to sleep and they are fighting being inwards - try a hip carry. Hip carries can be the best of both worlds - view out, space for baby to turn away if simulation gets too much and their head and neck is supported from behind making this a safe position for sleep.
-Madeleine