Lemme crank out my bird knowledge XD

First thing straight off the bat, I know this may sound cruel, but don't get upset if this bird dies. Being someone who has raised countless birds (wild and tamed) and rescued many birds, I can't guarantee that this baby bird will survive. And if the mother is alive then most likely she is to scared to return to her nest because you are there.
Now though I said that, DO NOT put that baby bird back in there because by now the mother would of completely abandoned it.
Also do not make loud noises in the same room as the little darling. IT MIGHT DIE OF FRIGHT, literally. Or just be scared witless.

Now a nice trick we do when it comes to feeding young birds (especially ones who gape) is soaked cat food. You need dry cat food and soak it in luke-warm water until squishy. Then you get plastic tweezers and put them to feed the baby bird. However a bird at first might need coaxing and encouragement as they will not understand/be scared. Unless they are like the Jackdor baby we rescued named Dorson who gulped food down XD
I also recommend to have a small bowl (with a couple of rocks in) filled with water so the darling can drink.

Now you may need to buy a incubator (a cheap one preferably) as they are extremely food at keeping young birds warm. If you don't want to buy one I can advice buying a heat lamp and setting up a small caged area with one fluffy towel at the bottom with the heat lamp over the top. This is a safe, warm enviroment for a young bird.

Now if the young bird constantly has it's beak slightly parted that might mean you need to feed it or it is thirsty. This is also the same if you hear peeping which might also just be a company-craving thing.
Another tip is not to handle this young bird to much. This can make them stressed and having strange things picking them up can be very scary for them.

At night (or early/late morning) I recommend putting a cloth over the cage so the baby can get some sleep. After all, it is still a young bird.

Now if this darling does grow big and strong you should try and release it into the wild. However, if it comes back this bird is then tamed and you can keep them as a small pet XD
If that happens, try potty training them XD


EDIT: Something else to note, the darling might seem perfectly fine for some time but might randomly die. I know that is random but the darling may have worms and won't absorb any nutrients. That or it was to malnourished to be rescued in the first place. This happened to Dorson, so this is just a heads up to expect death even if the darling seems fine.

Oh, thanks for all this help, XD.
But it is of no use as of now.
Me and my mom got scared of mites and later our family had an argument about it. Just today, I woke up and my mom said she put the nest on a big tree in our front yard. The mom soon found the baby and they reunited. Unfortunately, the nest was very unstable there and the nest came crashing to the ground, along with the hatchling!! Thankfully, it is perfectly fine, just a little frightened. My dad put the nest and the baby back in the bucket, and nailed it down to the tree. He added a twig for the mom to perch on when feeding, and a ceiling above the bucket so predators can't see him and make him end up like his siblings. However, he is up higher than before and if he jumps out he has a bigger chance of getting hurt, and there is no big branch underneath the bucket so that when jumps out he will have nothing to safely walk on, for when he gets older.