The cage is his "safe space". If birds haven't been handled from the time when they were very young, they don't develop the friendliness and eagerness to be with humans, so, they have to be trained and have their fears replaced with anticipation of good things happening for them.
If your bird will accept treats from your fingers, then clicker/target training would likely be the best solution for you. I've found most clickers to be too loud though, which scares my birds, which isn't the response you want to have as you don't want to instill fear in your bird every time you click the clicker. I've found the light click that a pen makes works far better than any of the clickers sold as training devices I've found. The click of a pen is quiet enough not to scare a skittish bird, but is still loud enough to serve as a training tool.
There are a lot of videos available on how to use a clicker and a target stick to train a bird to perform desired behaviors. In the case of a bird that doesn't want to come out of their cage, you first begin introducing a target stick near them, just to get their curiousity going. Their natural instinct is to try to test the stick with their beak and tongue (chopsticks work well for this purpose). This is the way birds investigate and discover their world. you hold the clicker (i.e. the pen) in the same hand as the target stick, and when the bird touches the stick, you click at the same moment, and then you offer a treat. You keep repeating this until the bird begins to realize that touching the target stick with their beak or tongue gets them a reward. Once they realize this, they look forward to touching the target stick.
Once they are used to touching the target stick and associate it with getting a reward, you then begin moving the target stick just a little bit, like an half inch or an inch, from them so they have to make a little effort to touch the target stick. ALWAYS offer a treat every time they touch the target stick with their beak and/or tongue. This is very important.
Once they understand they have to touch the stick to get a reward, and they have to make a little effort to touch it, then you start moving the target stick just a little further away, like 2" away, so they have to make a little more effort. As they begin to understand they will be rewarded for making the effort to get to the target stick to touch it, you're nearly ready to accomplish your goal. It may take several days to accomplish this. But it's important to go at your birds pace, and to keep your training sessions limited to not more than 10-15 minutes so you don't fatigue your bird. If you do that, they won't look forward to the next training session. You always want to end your training session while your bird is still performing well, still interested, and still showing an eagerness to do what you're asking of them.
Once your bird understands it has to make a little effort to touch the target stick, wherever the target stick may be, to the left, the right, or just above and in front of them (don't do down, as it's too difficult for them to reach lower than they are), then you gradually move the target stick closer and closer to the door. Don't be in too much of a hurry to get them to reach for the target stick outside of the cage, and pay attention to what your bird is comfortable with.
As you work with your bird over several days, you should begin to get a feel for how much progress your bird is comfortable making. Getting them to the point of getting close to the door to touch the target stick is close enough for a day or two to establish their comfort with being close to the open cage door. Only when they're comfortable being close to the cage door and showing no signs of running away should you finally move the target stick like an inch outside of the door, and when they step out onto the door and touch the stick, give them their treat.
By doing this target stick training and offering a treat, you teach your bird to focus on the target stick to get a reward, and they no longer focus on whatever was bringing up fear for them. You can eventually just show them the target stick outside the door and they'll make a beeline for the stick so they can touch it to get their desired treat.
You can also use the target stick/clicker training to teach your bird to "step up", as well as many other desirable behaviors.