It is not possible. Infact God cannot be proved using tarka.
Refer to Brahma Sutra and its Bhashya by Adi Shankara Acharya
Brahma-Sutra 1.1.3: Sanskrit text and English translation.
शास्त्रयोनित्वात् ॥ ३ ॥
śāstrayonitvāt || 4 ||
śāstrayonitvāt—The scripture being the means of right knowledge.
- The scriptures (alone) being the means of right knowledge (with regard to Brahman, the proposition laid in Sutra 2 becomes corroborated).
This Sutra makes the idea expressed in Sutra 2 clearer. If any doubt has been left regarding the fact that Brahman as the origin etc. of the world is established by scriptural authority and not by inference etc. independently of it, this Sutra makes it clear that Srutis alone are proof about Brahman