dnd 5e: What methods are there for your CA to exceed 20 without magic elements?

Heavy plate / Shield gets you 19
Lvl 6 Forge Domain Cleric grants you +1 AC and access to Ceremony and Revivify and Shield (More on this later)
Lvl 1 Fighter gives you a fighting style Defend for +1 AC

Capture / pay / convince a small humanoid and perform Ceremony (Marriage) between the two of you for +2 BC for 7 days, provided you are within 30 feet of each other.

At the end of the week, "widow" yourself and revitalize your spouse's body and remarry. Bonus points can be revived so as not to grow back limbs, tongues, etc., so you can eliminate the limbs and get a silent and small quadriplegic that can easily fit in your backpack.

Also, you get the spell shield, so you have a reactionary AC +5 in your back pocket (along with your spouse).

Keeping your spouse linked to you also provides coverage, so there is another AC +2.

So, at level 7 you can have 25 (30) AC.