This website notes a connection and writes as follows:
The term טבע to denote “nature” is derived from:
Prov. 8:25– Before the mountains were sunk within the water;
Metz. David… sunk in the sense of established/planted;
Ibn Ezra… as in: on what were its sockets sunk (הטבעו), or who laid its cornerstone (Job 38:6).
RSRH Ex. 15:4(paraphrased) – טבע means ...
The Shem miShmuel answers your question, he says:
ואדמו"ר זצללה"ה הכהן הגדול מאלכסנדר אמר כי לשון טבע הוא מלשון טובע
בנהר, שאדם צריך שמירה שלא יטבע בגשמיות
Translation (I do not know how to translate the abbreviated titles):
"...said: Because the word טבע (nature) is from the word טובע
(drowning) in a stream, that a person needs gaurding in ...