He needs to be under 23 and dependent. I cannot give more advice without being engaged and furnished with all material.
How can I include my son in my 888 visa application if he is 22 years old?
Our family applied for 188 visas right before my son turned 18 years old. More than four years has passed and now we need to apply for 888 permanent visas. However, my son is already 22 years old and just started his first job. Is he still eligible to apply for the 888 visa with us? If not, is there any way that he can stay in the country?
If your son was included in the subclass 188 application then he is able to be included in the subsequent subclass 888 application even if his circumstances have changed in a way that would normally exclude him as a member of the family unit (e.g., working and no longer a dependent child). This is done to cover situations such as you have mentioned. (Separately, do note that a single 22-year-old can still be a dependent child if not working.)
Apply before 23 years old. Make sure your son is still dependent. His eligibility is important or else one fails, all fail. This requires careful analysis of your circumstances. I would engage a lawyer before lodgment in case your son is not eligible.
If secondary provisional 188 visa holders are no longer dependent family members of the primary provisional visa holder by the time of application for 888 permanent residency, under the member of the family unit regulations, they are still deemed to be family members of the primary provisional visa holder for that permanent resident application, provided they are included as secondary applicants in that permanent resident application. This will apply as long as they were granted their 188 visa on the basis that the person was a member of the family unit of a person who held a visa of the same kind.