Welcome to the forums!
You have certainly come to the right place as you will find all you need to know on budgie care here.
The information on the articles and sticky threads at the top of each section of the forums will be very useful and of benefit to you and your budgies.
Is this room bird proofed as in completely safe for your budgies?
I'm asking this because if no one is there to supervise (since they are out for most of the day), they may get in trouble.
Another important aspect you need to consider is your own lifestyle and how a possible change can deeply impact your budgies' routine.
If for example there is a change in your life (a new job, moving into another house, or any other type of personal matter) which may have repercussions and directly influence the time/availability you have for your budgies.
Potential vacations where you will either have to board your budgies or have them at a friend's house could be very troublesome if they are used to so much freedom and they can very well react badly when there is the need for them to be on their cage for a longer amount of time.
It would be good to establish a more balanced routine for your budgies when it comes to the time they have inside the cage and out of it.
It would be easier for you to hand tame them while in the cage, since this is more of a confined area. First of all, it's important to establish the foundations of trust and this is done by getting them used to your presence and voice. Once they show signs of being receptive to you (by moving closer to you), you can then proceed to offer them a little tasty treat to eat in order to encourage them to step onto your hand/finger. With continued training sessions, in due time they will step onto your finger when asked and then it will be easier for you to take them out and place them back into the cage without waiting for day's end.
At this point and since your budgies aren't yet finger tamed, you can try to carefully lead them back to the cage by using one of the perches from the cage. Most likely your budgies will automatically step onto the perch the moment they see it and then you can guide them to the cage.
This section has lots of good info and tips on how to train your budgies and on how to build a long-lasting bond with them.
Be sure to check the stickies at the top of the Taming and Bonding main page.
You can start with this one: https://talkbudgies.com/taming-bondin...-training.html