Both mithral armor and adamantine armor are listed as uncommon magic items. In the guidance on crafting a magic item in the Dungeon Master’s Guide (p. 128-129), uncommon magic items have a range of value of 101-500 gp.
Obviously, mithral plate is not worth less than mundane plate armor, so at my tables we have always just added 500 gp to whatever the value of the mundane version of the armor is to get the value of the mithral or adamantine versions. This has always been well-received by players I’ve played with, and is consistent with the accepted answer to the related question What would be the price of Adamantine Plate armor?
Time is going to be largely up to the DM. There is some guidance in Xanathar’s Guide to Everything concerning crafting magic items (p. 128-129); the suggested crafting time for uncommon magic items is two weeks (and 200 gp of other expenses).
Bringing it together
If I’m running the game, I’ll let you buy mithral plate armor or adamantine plate armor for 2000 gp. But if you want to craft it yourself, or that is the avenue your DM has determined for you to take, I would suggest following the guidance on crafting an item in Xanathar’s Guide to Everything (p. 129):
An item invariably requires an exotic material to complete it. This material can range from the skin of a yeti to a vial of water taken from a whirlpool on the Elemental Plane of Water. Finding that material should take place as part of an adventure.
I will work the mithral or adamantine raw materials into the adventure or allow the player to purchase 500 gp worth of it, then allow the player to craft the mithral or adamantine variant of an existing armor during two weeks of downtime.