Welcome to the forums, GCCs are great little birds.
For talking first realize that a GCC will not likely ever talk like a grey or a macaw. Some happy healthy conures never learn to say much of anything, but they certainly can and many will pick up a few words over time
If you want to encourage his speaking abilities there are a few things you can do. One suggestion is to record your voice saying something and set it to play back on repeat so he hears the word over and over again. While this can work I am not a fan of this method for a couple reasons I will address in a moment. One aspect of this method that is worth noting is that it is to increase the salience of the word. Parrots pick up on the most significant, salient, or 'meaningful' sounds. There is more than one way to increase the salience however and repetition may not be the best way.
The best way to increase the salience of the word is to use it in context and with "feeling". There is a reason many birds learn to laugh quite easily even if other words take time. Laughing may not be heard more often but it is more emphatic. Laughing is associated with a whole set of other behaviors and expressions that signal its significance. This is why parrots also pick up on "bad language" far faster than any owner would want them to.
Parrots also often learn various "kissing sounds" for similar reasons. In addition to the emotional aspect of kissing sounds there is also the social context. Most people don't make kissing sounds at random around their bird, they do so when they get close and usually touching. This social context gives the sound more meaning and salience so it is easier for them to learn.
Now for what I see as problems with the simple repetition method: First off it can work quite well... depending on how you define 'working.' The bird may start saying the word quickly, but the word will have no meaning at all. This is not a form of language in any way, it is just "parroting" (which is a bad name as parrots do not actually do it very often).
The first problem with the repetition method is that it can sometimes be counterproductive to actually learning the repeated word. The repeated word becomes like background noise - by habituating to it it will be a familiar sound but it will be learned as something that has zero meaning. If it means nothing why try to say it?
Secondly is, as already alluded to, that at best they will simply learn to say the word. Most of us would prefer our birds can use words meaningfully which can only be done by learning them in context.
So, I recommend making particular words part of your interaction with Mikey. Emphasize the words you want him to know. Associate them with the appropriate emotional or social contexts, and as much as possible exaggerate these contexts.
Also realize that birds vocal learning flows in two stages - they do not simply repeat what you say. First is the sensory phase where they listen. They listen and they start forming a mental 'sound-image' of words that seem important. Then is the sensory-motor phase where they experiment with sounds or 'babble' and fine tune their babbling until it sounds similar to the previously acquired mental 'sound-image.' This means that you should not get them to say something CLOSE to the word then change it by fine tuning the cue you give them as by the time they start trying to produce a word they already have a complete 'image' of what it should sound like memorized. This also means just because he isn't trying to mimic on a given day does not mean he is not learning. In fact I have often seen Auggie look quite curiously in response to an interesting sound or word - he will not try to mimic it then and there, but these are the words he will later practice.
Anyhow, to boil this down my recommendations are: 1) be patient and don't be disappointed it Mikey doesn't become much of a talker; 2) use words you want him to know in context and emphatically; and 3) realize that his 'word-production' may come several months after his 'word learning', so even if he is not making any attempt to mimic yet he will still likely be learning words.
