My kid has started to roll over to his tummy from lying on his back. He currently sleeps in a bassinet. He has not fully rolled over yet. We are worried is it safe if he rolls over completely during night after he is put to sleep and we are asleep. Will he go on to his tummy, have his nose pressed against the bassinet mattress and hence impeding his breathing? If he cries, we are awaken and put him back to his back. What if he doesn't? Any advise?

Most babies will be rolling over by 4- 6 months….. some earlier, some later.
This is very normal as babies grow & become stronger.
Many babies then prefer to sleep on their tummy.
This is not something that needs to be stopped. It is important to make this new environment as safe as possible.

Your baby needs to be moved to now sleep in a cot - not bassinet.
Ensure that the mattress is firm & flat & there is nothing soft or loose in the cot.
Always place baby on back to sleep.
Increase tummy time when awake.
How does he go with tummy time? Is he lifting his head & look around?
If you are still wrapping your baby, this need to be ceased - he needs his arms free.

Red Nose has the following information now that your baby is starting to roll.

Give baby extra tummy time to play when awake and supervised as this helps baby to develop stronger neck and upper body muscles which in turn enables them to roll back over.
Make sure that baby is on a firm and well-fitting mattress that is flat (not tilted or elevated).
Make sure that baby’s face and head remains uncovered (do not use lambswool, doonas, pillows, cot bumpers or soft toys)

As babies grow and develop they become very active and learn to roll around the cot.
At this time, continue to put them on the back at the start of sleep time, but let them find their own position of comfort.
By this stage it is not necessary to wake during the night to turn baby over to the back position

Do not use any devices designed to keep baby in a particular sleep position.
https://rednose.org.au/article/what-do-we-do-now-that-a-baby-has-started-to-roll-over