I have hand-tamed literally dozens and dozens of parent-raised, non-tame Budgies throughout my life, along with other parent-raised, non-tame species of parrots, and I can't tell you how much horrible and just plain WRONG advice on training/taming and bringing home a new bird there is out there, especially on the internet and on sites like YouTube...A few of the most horrible pieces of advice include:
-When you bring home a new baby bird, don't pay any attention to it at all and just leave it alone for at least a week or two, if not longer, so it can "settle in" to it's new home...(HORRIBLE ADVICE)
-When you bring home a new baby bird, don't let it out of it's cage at all for at least a few weeks to a month, because it needs to settle-in
And what you just wrote, "Don't ever take your new bird out of it's cage until after it's already stepping-up for you and is a bit hand-tamed" is probably the worst piece of advice I've seen, simply because each bird is an individual and totally different than the next, and you have no idea how territorial they are going to be about their cage...So if you were to keep trying to hand-tame your Budgie and get him to step-up for you while still inside his cage, and to not allow him out of his cage UNTIL AFTER he's already stepping-up and hand-tamed, THAT MAY MEAN THAT YOUR POOR BUDGIE WON'T BE ALLOWED ANY OUT-OF-CAGE-TIME FOR WEEKS TO MONTHS TO EVEN OVER A YEAR!
Obviously that's ridiculous, or at least it should sound ridiculous to you, because you can't bring home a new baby parrot and not allow it to come out of it's cage at all for potentially months and months! It's not healthy for the bird, neither physically or psychologically, and it's not going to get you anwhere with his hand-taming or training at all, because obviously he is at least a little territorial about his cage...So it's a "Catch-22", because "You can't take your new Budgie out of his cage until he's already hand-tamed and stepping-up for you, but he'll never become hand-tamed nor step-up for you while he's inside of his cage because he's too focused on your hands being inside of it."
*****There was a new member here a couple of months ago, I believe they wrote this post I'm remembering in January or December, that is a great example of what I'm talking about...This new member had a Cockatiel, and they were posting because they thought that something might be wrong with it, I think it was a hurt foot or something like that...But when we asked him to post some photos of their Cockatiel, they stated that their Cockatiel, who was 4 years-old at this point and who they had originally brought home as a young baby under a year-old, HAD NEVER ONCE BEEN OUT OF IT'S CAGE because they weren't ever able to hand-tame him or get him to step-up while trying to work with him inside of his cage, so they couldn't take photos of him and didn't want to take him to an Avian Vet because he had never once been out of his cage in the entire 4 years they'd had him!!! This is exactly what can happen if you approach hand-taming/training a young baby parrot who was parent-raised and not ever handled by people by not allowing it to come out of it's cage until AFTER it's hand-tamed and already stepping-up for you, the bird will never become hand-tamed nor be stepping-up, so the bird never comes out of it's cage!!! And you don't want that...
***Step #1 to hand-taming a parent-raised parrot is ALWAYS going to be EARNING THE BIRD'S TRUST, because the bird will not ever step-up for you or allow you to handled him/touch him if he doesn't trust you...Right now the only thing that he trusts is being inside of that cage, his "safe-space". So, there are a couple of different ways that you can approach this situation, but all of them are going to involve you allowing him to come out of his cage in a safe room with a shut-door, and then removing his cage from the room so that it's totally out of his sight and he can't go back to it...
The easiest and quickest way to hand-tame a parent-raised, non-tame Budgie, is to have his wings clipped with a CONSERVATIVE CLIP that will completely grow-out allowing the Budgie to fully fly again in about 2 months or so; this gives you about 2 months to take advantage of, to spend time every single day working with him, so that in about 2 months when his wings grow back in fully and he can fly again, he'll already not only be stepping-up for you every time you simply put your finger down against his lower belly for him, but he will also fully trust you and allow you to handle him, and want to hang-out with you outside of his cage without constantly flying away from you.
A lot of people are totally against clipping a bird's wings, but in this case, it doesn't matter either way whether your Budgie's wings are clipped or not because he's not coming out of his cage at all and flying anyway! So why not have his wings clipped conservatively, giving you 2 months to get him out of his cage every single day for a good amount of time? He isn't flying anyway as things are, and I can guarantee you with 99% confidence that if you do clip his wings conservatively and you commit yourself to getting him out of his cage every single day and working with him one-on-one, that by the time his wings grow back-in in about 2 months you'll have earned his trust fully, and you'll be able to handle him, have him step-up, have him liking/wanting to sit on your shoulder and to just be with you whenever possible, etc. Now you still will need to remove his cage from his sight when you first start working with him, because he will still be wanting to get back to it constantly, but the difference is he won't be flying away from you continuallly, with you chasing him all over the place...
I highly recommend you give the wing-clipping a try, like I said, in this situation, you're not taking the ability to fly away from your bird because he's not being taken out of his cage at all anyway, and it's only going to be a very temporary, 2-month period that should be extremely productive for you and will allow him to actually BE ALLOWED TO FLY when the wings grow back in, because he won't be flying away from you constantly, you'll have earned his trust, bonded with him, have him stepping-up for you regularly, and also hopefully have him Recall-Trained so that he wants to come to you whenever he's out of his cage...You just have to make sure that you tell whomever clips his wings (Avian/Exotic Vet, Bird Breeder, or even a bird-shop/pet shop employee/owner who you're sure knows what they're doing) that you Only want them to clip the outermost 5-6 Primary Flight-Feathers on BOTH wings. That's it, and this is totally painless, and if you make sure you request this then he'll be flying again in about 2 months as a hand-tamed bird.