Teva as "nature" - i.e. the natural world - begins to appear in Ibn Tibbon's translation of the Rambam's Moreh Nevuchim. In the section on the foreign words used in the book, Ibn Tibbon writes (from this translation):
Nature [teva'] is a term that has many meanings, especially in our language, especially since I use it in place of two different Arabic terms, which themselves have different meanings. The one is tabi'a, and the other tab'. ... The philosophers already explained these two terms and the meanings each possesses. What we need to mention here are only the following: One says 'teva' with reference to the principle of any change, persistence or abiding ... any power that exists in a thing always, without changing, is called 'teva'.
The broader sense of "form, shape, character, essence" appears occasionally in Talmudic Hebrew, where it also is the name of a coin, with the value of half a sela. Jastrow provides one example of the meaning "element" from Bamidbar Rabba 14, and then untypically adds "in later Hebrew: nature, character; Nature." The general word for coin - matbe'a מטבע - is related (coins were made by impressing a design on a piece of metal), and it too can also mean "type, formula".
Ilana Goldhaber-Gordon points out in this article in the Forward, an interesting change in the connotation of teva:
Today, the connotation of “teva” has flipped, as the omnipotence of God has receded in the face of science and technology. “Natural” no longer stands opposed to “divine,” but to “artificial.” Teva is wild and free, like gurgling brooks and rushing rivers; its opposite is human-built, like the network of pipes that brings fresh water to our homes.This certainly seems true. I imagine that if you were to perform a survey of Israelis today, and ask them whether the adjective tiv'i טבעי means "with form" or "without form", they'd overwhelming choose the latter.
Both teva and matbe'a derive from the Biblical root טבע - "to sink, drown", which can also mean "to impress, stamp, coin." Klein writes that the name of the Hebrew month Tevet טבת may derive from this root as well: originally from the Akkadian tebetu, "it means perhaps literally 'month of sinking in' (i.e. muddy month)".
But what about the Biblical word taba'at טבעת - "ring"? Is it also related?
Most authorities think so. Their assumption is that taba'at originally meant "signet ring", which was used to impress a seal on wax or clay. (Others say that taba'at derived from the Egyptian d.'bt or gb'.t meaning "seal", and therefore may not be related to טבע). This type of ring was used as a signature, and so if the taba'at of the king was given to someone (e.g. Pharoah to Yosef in Bereshit 41:42, Achashverosh to Haman and Mordechai in Ester 3:10, 8:2), it was a sign of transfer of authority.
However, we also find taba'at with the more general meaning of "ring", in the description of the utensils of the Mishkan, for example in Shemot 25:12. (Certainly these rings were not signet rings, although such rings were donated to the Mishkan, as in Shemot 35:22 - see Cassuto's commentary there.) This seemed difficult to me, for I would assume that first plain rings (not signet) were invented (for jewelry or other purposes) and only later signet rings. The same - in my mind - would apply to the development of the word as well. Some try to explain this difficulty by saying that the root טבע in taba'at didn't refer to impressing the seal, but rather the ring was made by "pressing in". But that explanation is hard to accept, since even the verse discussing producing rings for the Mishkan uses the verb יצק - "to pour", not "to press".
I think a better explanation may be that everything used in the Mishkan was "special" (or perhaps "royal"). We see use of materials like techelet תכלת, which have special religious significance, and even the "holy" shaatnez שעטנז, is frequently found in the garments and other utensils in the Mishkan. So perhaps from "signet ring", taba'at came to mean "special, royal ring" - and that is why it was chosen over some other, more common synonym.