I agree that the conditions your flock is kept in aren't ideal for you to let them safely breed. It's important to establish a routine for your flock and to keep the time they spend in and out of the cage balanced.
Even for a bird proofed room, accidents can still happen when the budgies aren't being supervised.
From your other thread you created back in November you mentioned being new to budgies: i bought 4 budgies
Before taking the breeding route and in order to do so more safely, a person should have a very good grasp of the species (this comes with real life experience in budgie ownership) and to do the required research into the subject.
The decision to breed comes with a whole lot of responsibility and commitment, the lives of the breeding pair(s) and the chicks are depending on you and the response you give if/when faced with adversity.
Things like being able to tell if your breeding pair is in good health and top physical condition to go through breeding; when a hen is expecting an egg or if she is showing the first signs of being egg bound; when a chick is having developmental problems, not being fed or showing signs of dehydration;
when there is aggression, abandonment and neglect of the chicks and it's solely up to you to feed and raise the chicks. The ability to detect early on and solve these issues can truly make a difference on the outcome of your breeding journey.
Also the photos you have posted in that thread indicated that your budgies were very young at about 3 months old. There is no way that after two months they are 1 year old and at the very minimum required age to breed.
For your budgie's overall welfare, please remove the nest box, your female is much too young to be put through egg laying and her life will be at risk.
Follow the recommendations on the links previously given to you and at this point separate your female from her mate.
Your flock needs structure, not chaos where they are left alone in room allowing the conditions of a colony breeding setting. Remove all hiding places and nesting sites from the room and cages as well.
If need be, house your budgies separately by gender.
This is a less than desirable situation that needs to be addressed urgently.