No, you need 5 minutes to doff plate armor. You could use illusion or possibly transmutation to create the appearance of armor. To persuade your DM to have easy-off armor you might have to pay a real world or game world cost.
Long answer follows..
The RAW say that Heavy Armor takes 5 minutes to doff (PHB 146), so instant doffing not possible.
You also can't teleport out of it, because as you say you can't cast spells in it.
It sounds like you don't actually want to use the armor as armor (you want to take it off as soon as combat begins), so why not just create it as an illusion? As an example, Disguise Self seems to do the trick. It's a first level spell too, so much 'cheaper' than teleport! If you're high enough level to be using seventh-level spell slots then your spell save DC is going to be quite tough to beat (in terms of others seeing through the illusion).
You make yourself — including your clothing, armor, weapons, and other belongings on your person —look different until the spell ends or until you use your action to dismiss it.
Even so it would take your first action of the combat to dismiss the illusion. However, you could use a Hat of Disguise (DMG 173), and in that case it would just be a case of taking off the hat, a free action:
While wearing this hat, you can use an action to cast the disguise self spell from it at will. The spell ends if the hat is removed. (DMG 173)
If you would prefer not to use an illusion, you could use a transmutation spell. For example, you could see if your DM would let you use Alter Self, though the wording of the spell is unclear as to if you can actually create the appearance of armor.
You transform your appearance. You decide what you look like, including your height, weight, facial features, sound of your voice, hair length, coloration, and distinguishing characteristics
"Clothing and armor" are not mentioned, so your DM would have to rule this one.
Persuading your DM
If you really want to go with armor which falls off quickly (which is a hilarious image!), there are two basic ways to convince your DM:
- Real world: make them cookies, do their laundry, etc.
- Game world: pay enough GP, go on a quest to find a suitably qualified inventor (a Dragonlance Gnome Tinkerer springs to mind), do it yourself (using Smith's tools), etc.
In any case your DM can put serious limitations on the fake armor, like it's difficult to move in, or one hit and it falls off. Your DM might also refuse outright if it doesn't fit the tone of your campaign.